text:
\section{Introduction}

Study on strongly correlated electrons opened a new window so
called gauge theory in modern condensed matter physics. When
electrons are weakly correlated, that is, kinetic energy is more
dominant than potential energy, a local order parameter approach
is available based on decoupling of interaction channels. This is
the heart of "classical" condensed matter physics composed of
Fermi liquid theory and Landau-Ginzburg-Wilson framework. On the
other hand, when interactions are strong enough compared with
kinetic energy, an infinite interaction limit can be a good
starting point. The presence of such a large energy scale gives
rise to a constraint in dynamics of electrons. In addition,
interesting physics now arises from the kinetic-energy
contribution in the restricted Hilbert space, and "non-local"
order parameters or more carefully, link variables instead of
on-site ones in lattice models appear as important low energy
collective degrees of freedom. These link variables can be
formulated as gauge fields, and gauge theory arises naturally for
dynamics of strongly correlated electrons.

In the present study we revisit a doped Mott insulator problem
based on one possible gauge theory approach of the slave-fermion
representation. The slave-fermion representation relies on the
fact that a spin degree of freedom of an electron is represented
by a bosonic matter, thus it is advantageous in describing
magnetic ordering of localized moments via condensation of bosonic
spinons while it has difficulty in connection with Fermi liquid.
On the other hand, the slave-boson approach resorts to the fact
that a charge degree of freedom of an electron is represented by a
bosonic matter, thus the slave-boson gauge theory has its clear
connection with the Fermi liquid theory via condensation of
bosonic holons while it does not have a "natural" description for
ordering of localized magnetic moments, compared to the
slave-fermion approach.\cite{Heavy_Fermion} An immediate question
is about statistics of spinons. At present, there is no clear
connection between the fermionic and bosonic descriptions for spin
degrees of freedom.\cite{SO5WZW}

The problem to determine which of the representations is available
seems to be associated with the nature of an undoped parent Mott
insulating phase. Although there is no obvious way to classify
undoped Mott insulating phases, it is natural to consider
symmetric and symmetry-broken Mott insulators.\cite{S_SB_MI}
Symmetric Mott insulators are usually called spin liquids, where
both fermionic\cite{PALee_Review} and bosonic\cite{Sachdev_Review}
spin descriptions are available. Symmetry-broken Mott insulators
can be discriminated further, depending on their symmetry breaking
patterns. An example of translational symmetry-broken Mott
insulators is a Mott insulator with a valence bond solid order,
and that of rotational symmetry-broken ones is an
antiferromagnetic Mott insulator. Bond-operator
formalism\cite{Sachdev_BOP} may be useful for the description of
the valence-bond-solid Mott insulator while the antiferromagnetic
Mott insulator will be described well by the Schwinger-boson
representation\cite{Book}.

In this paper we focus on doping to an antiferromagnetic Mott
insulator based on the slave-fermion approach. In early days
single-hole dynamics in the antiferromagnetically correlated spin
background was one of the main interests.\cite{SF_OLD} Hole doping
frustrates an antiferromagnetic spin configuration. Interactions
with such antiferromagnetic fluctuations give rise to a
self-energy correction of a single-hole, resulting in the fact
that it resides in four diagonal momentum points of
$(\pm\pi/2,\pm\pi/2)$. Mathematically speaking, the hopping term
in the slave-fermion representation of the t-J model, usually
called the Shraiman-Siggia term in the continuum approximation,
plays a crucial role for the single-hole dynamics. In the present
paper the role of this term is critically reinvestigated, and we
find that it plays an important role for dynamics of both holes
and spin fluctuations.

Recently, this problem was revisited by several authors, claiming
that the slave-fermion approach allows an anomalous metallic phase
with short-range antiferromagnetic correlations, where bosonic
spinons are gapped away from the antiferromagnetic Mott insulating
phase.\cite{ACL,BCS_Hubbard} An effective field theory for the
doped antiferromagnetic Mott insulator was argued to be a
non-relativistic fermion (holon) U(1) gauge theory for charge
dynamics (of gapless charged fermions around the four diagonal
points) and a relativistic boson (spinon) U(1) gauge theory for
spin dynamics (the CP$^{1}$ gauge theory of the O(3) nonlinear
$\sigma$ model for antiferromagnetic spin fluctuations), allowing
an anomalous metal phase when bosonic spinons are
gapped.\cite{NFL_SL} The presence of such an anomalous metallic
phase is attributed to
deconfinement\cite{Deconfinement_Senthil,Deconfinement_Kleinert,Deconfinement_Kim}
of compact U(1) gauge theory, where the presence of gapless
fermionic matters is expected to suppress monopole
(skyrmion\cite{Skyrmion}) excitations in two space and one time
dimensions [$(2+1)D$] although the pure compact U(1) gauge theory
does not allow such a deconfinement phase in
$(2+1)D$\cite{Polyakov}.

From a microscopic point of view, the emergent U(1) gauge
structure can be allowed when hopping of spinons and holons
between next nearest neighbor sites, i.e., hopping between same
sublattices in the square lattice has its nonzero vacuum
expectation amplitude while hopping between different sublattices
(nearest neighbor sites) vanishes in the presence of short-range
antiferromagnetic correlations (spinon singlet-pairing order). In
the present study we reexamine the spinon-holon exchange hopping
term carefully, and reveal that the emergent gauge structure is
Z$_{2}$ instead of U(1) owing to the fact that hopping of doped
holes frustrates the collinear antiferromagnetic spin
configuration and results in a complex magnetic structure. Such a
complex spin texture is reflected in nonzero expectation values of
nearest-neighbor hopping parameters of spinons and holons. In
other words, dynamics of doped holes enhances ferromagnetic spin
fluctuations, reducing the U(1) gauge symmetry, arising in the
case when only collinear antiferromagnetic correlations are
considered, down to Z$_2$.

For definiteness, we first consider the antiferromagnetic
Heisenberg model based on the Schwinger-boson representation. In
this study we allow both ferromagnetic (exchange hopping of
spinons between different sublattices) and antiferromagnetic
(singlet pairing of spinons between different sublattices)
correlations. In addition, emergence of a flux is admitted for the
ferromagnetic exchange-hopping channel. Based on the saddle-point
analysis for magnetic ordering, we find; (1) If no flux is allowed
in the exchange-hopping parameter, the vacuum expectation value of
the hopping parameter vanishes, thus our mean-field analysis
recovers the conventional Schwinger-boson mean-field theory for
collinear antiferromagnetic ordering.\cite{Book} The resulting
effective field theory is a relativistic U(1) gauge theory, i.e.,
the CP$^{1}$ gauge theory of the O(3) nonlinear $\sigma$
model.\cite{Sachdev_Read} On the other hand, (2) if $\pi$-flux is
allowed in the hopping channel, the hopping parameter between the
different sublattices has its nonzero vacuum expectation value
because the presence of $\pi$-flux enhances ferromagnetic
correlations. As a result, the U(1) gauge symmetry is down to
Z$_{2}$ since both spin-singlet pairing and exchange hopping
exist. The presence of both antiferro- and ferro- magnetic
contributions causes the magnetic ordering structure to be
complicated. We discuss physics of this possible complex magnetic
structure.

Next, we study a doped antiferromagnetic Mott insulator based on
the U(1) slave-fermion representation of the t-J model. As
discussed before, the main point is how to take the hopping-t term
into account. Performing the similar mean-field analysis as the
above, we find that the hopping parameter does not vanish even in
the uniform flux case owing to the fact that mobile doped holes
increase ferromagnetic correlations. As a result, a complex
magnetic structure such as a spiral type is expected to appear,
consistent with doping-induced spiral magnetic ordering of the
previous slave-fermion studies.\cite{SF_OLD} Enhancement of
ferromagnetic correlations induced by doped holes causes a serious
result that gapless U(1) gauge fluctuations do not exist in the
long-wave length and low-energy limits even when such bosonic
spinons become gapped to cause the fact that the spiral-type
complex magnetic structure disappears away from half filling. As a
result, this spin-gapped anomalous metallic state, where only
charge fluctuations are gapless exhibiting so called spin-charge
separation, is described by a Z$_{2}$ gauge theory instead of a
U(1) gauge theory. In this respect such a deconfinement phase is
certainly possible for $(2+1)D$, considering that even the pure
Z$_{2}$ gauge theory without matters allows its deconfinement
phase in $(2+1)D$.\cite{Fradkin_gauge_theory} We propose this
gauge-symmetry reduction in the low energy limit as one possible
mechanism for spin-charge separation in the doped
antiferromagnetic Mott insulator.

\section{Antiferromagnetic Mott insulator}

\subsection{Schwinger-boson mean-field analysis of the
antiferromagnetic Heisenberg model}

We consider the quantum antiferromagnetic Heisenberg Hamiltonian
\begin{equation}
\frac{H}{J}= \sum_{ ij } \vec{S}_{i} \cdot \vec{S}_{j} .
\end{equation}
Generally speaking, one can decompose the spin-exchange
interaction $\vec{S}_{i}\cdot \vec{S}_{j}$ with Schwinger-bosons
as follows,

\emph{(i)}  N\'{e}el scheme,
\begin{equation}
\vec{S}_{i} \cdot \vec{S}_{j} = -2\Delta_{ij}^{\dagger}\Delta_{ij}
+S^{2}
\label{eq::Neel}
\end{equation}

\emph{(ii)} Spiral scheme,
\begin{equation}
\vec{S}_{i} \cdot \vec{S}_{j} = -\Delta_{ij}^{\dagger}\Delta_{ij}
+ \chi_{ij}^{\dagger}\chi_{ij}-S/2
\label{eq::Sprial}
\end{equation}
where
$\Delta_{ij}=(b_{i\uparrow}b_{j\downarrow}-b_{i\downarrow}b_{j\uparrow})/2$
and
$\chi_{ij}^{\dagger}=(b_{i\uparrow}^{\dagger}b_{j\uparrow}+b_{i\downarrow}^{\dagger}b_{j\downarrow})/2$
are associated with antiferromagnetic and ferromagnetic
correlations, respectively.

In order to clearly show physical meaning of $\Delta_{ij}$ and
$\chi_{ij}$, it is convenient to consider classical spins. If we
choose two nearest neighbor spins
\begin{eqnarray}
b_{i}=\sqrt{2S}
         \left( \begin{array}{c}
                    1\\
                    0
                \end{array}\right),
~~~~
b_{j}=\sqrt{2S}
         \left( \begin{array}{c}
                    e^{-i\phi}\cos(\theta/2)\\
                    \sin(\theta)
                \end{array}\right) ,
\end{eqnarray}
where $(\phi,\theta)$ are spherical coordinates of spin $j$, then
\begin{eqnarray}
&& \Delta_{ij}=S\sin(\theta/2)  \\
&& \chi_{ij}=Se^{i\phi}\cos(\theta/2) \label{AB} .
\end{eqnarray}
For a ferromagnetic state ($\theta=0$), we have $\Delta=0$ and
$|\chi|=S$ while in the N\'{e}el state of $\theta=\pi$, $\Delta=S$
and $\chi=0$ result. In this respect $\Delta$ and $\chi$ represent
antiferromagnetic and ferromagnetic correlations, respectively.
Furthermore, for classical antiferromagnetic spins, when spins are
non-collinear (\emph{i.e.} $\theta \neq \pi$) where neighboring
spins have their finite overlap, $\chi$ becomes nonzero so that
$\chi$ describes canting and spiral. One may expect that
competition between antiferromagnetic $\Delta$ and ferromagnetic
$\chi$ correlations will give rise to non-collinear ordering in
the ground state of antiferromagnetically correlated spins.

Inserting Eqs. (5) and (6) into Eqs. (2) and (3),  we get
\begin{eqnarray}
& (\vec{S}_{i}\cdot \vec{S}_{j})_{N\acute{e}el} =  S^{2} \cos \theta \\
& (\vec{S}_{i}\cdot \vec{S}_{j})_{Spiral} =  S^{2} \cos \theta-S/2 .
\end{eqnarray}
It is obvious that the Spiral scheme is more favorite than the
N\'{e}el scheme  in the classical limit since it has lower ground
state energy. In the following we focus on the Spiral scheme.

\begin{figure}[b]
\begin{center}
\includegraphics[width=7cm]{Flux.eps}
\end{center}
\caption{Flux ansatz} \label{fig:Ek_flux}
\end{figure}

Taking into account the constraint of
$\sum_{\sigma}b_{i\sigma}^{\dagger}b_{i\sigma} = 2S$ at each site
via a Lagrange multiplier field $\lambda_{i}$, an effective
Hamiltonian in the Schwinger-boson representation of the
antiferromagnetic Heisenberg model can be written as follows
\begin{eqnarray}
\frac{H}{J} &=& -\sum_{ij,\sigma}\left( \Delta_{ij}^{*}\sigma
b_{i\sigma}b_{j\bar{\sigma}}+h.c.\right)
+\sum_{ij,\sigma}\left(\chi_{ij}b_{i\sigma}^{\dagger}b_{j\sigma}+h.c.\right) \nonumber \\
&+&
\sum_{i,\sigma}\lambda_{i}(b_{i\sigma}^{\dagger}b_{i\sigma}-2S)
+\sum_{ij}\left(|\Delta_{ij}|^{2}-|\chi_{ij}|^{2}\right) .
\label{AFH}
\end{eqnarray}
It is important to notice that the sign of the spinon-hopping term
is positive, implying that spinon-hopping contributions are
energetically unfavorable, thus its amplitude will vanish in the
uniform-flux case, as will be shown below. Physically speaking,
ferromagnetic correlations frustrating the antiferromagnetically
correlated background are prohibited in the naive mean-field
analysis. However, introduction of $\pi$-flux weakens such
frustration effects, ferromagnetic correlations contributing to
physics of antiferromagnetism.

For a mean-field analysis we replace $\Delta_{ij}$ and $\chi_{ij}$
with their saddle-point values. In the flux ansatz we parameterize
$\Delta_{ij}$ and $\chi_{ij}$ with
\begin{equation}
\Delta_{ij}= \Delta, ~~~~ \chi_{ij}= \chi e^{i\theta_{ij}}
\end{equation}
where $\theta_{ij}=\pm \theta$ if $ij$ along or against an arrow
in Fig. 1. Note that a flux is allowed only in the ferromagnetic
hopping channel. Based on this mean-field ansatz with $\lambda_{i}
= \lambda$, we obtain the following effective Hamiltonian in the
momentum space,
\begin{eqnarray}
&& \frac{H}{J} = -\frac{z\Delta}{2} \sum_{k,\sigma}\left( \sigma
\gamma_{k}b_{k\sigma}b_{\bar{k}\bar{\sigma}}+h.c.\right)
+ \lambda\sum_{k\sigma}b_{k\sigma}^{\dagger}b_{k\sigma}\nonumber \\
&&+ z\chi \sum'_{k,\sigma}\left(b_{k\sigma}^{\dagger} ~~
b_{k+Q\sigma}^{\dagger}\right) \left(\begin{array}{cc}
       \gamma_{k}\cos \theta & i \phi_{k}\sin \theta \\
       -i\phi_{k} \sin \theta & -\gamma_{k}\cos \theta
       \end{array}\right)
\left(\begin{array}{c}
       b_{k\sigma}\\
       b_{k+Q\sigma}
       \end{array}\right) \nonumber \\
&&- 2NS\lambda+\frac{z}{2}N\Delta^{2}-\frac{z}{2}N\chi^{2}
\end{eqnarray}
with $\gamma_{k}=1/z \sum_{j\in i}(e^{i k_{x}} + e^{i k_{y}})$ and
$\phi_{k}=1/z \sum_{j\in i}(e^{i k_{x}} - e^{i k_{y}})$. $z$ is a
lattice-coordination number, here $z=4$ for the square lattice.
The $'$ symbol in the momentum summation represents to perform the
summation in the folded Brillouin zone.

Performing the Bogoliubov transformation, we can diagonalize the
effective Hamiltonian as follows,
\begin{eqnarray}
\frac{H}{J} &=& \sum'_{k,s=\pm}\omega_{k}^{s}\left(
\alpha_{ks}^{\dagger}\alpha_{ks}+
\beta_{ks}^{\dagger}\beta_{ks}+1\right) \nonumber \\
&-&
2N\lambda(S+\frac{1}{2})+\frac{z}{2}N\Delta^{2}-\frac{z}{2}N\chi^{2}
,
\end{eqnarray}
where the quasiparticle spectrum is
\begin{eqnarray}
\omega_{k}^{s}= \sqrt{(\lambda
+sz\chi\Theta_{k})^{2}-(z\Delta\gamma_{k}/2)^{2}}
\end{eqnarray}
with $\Theta_{k}= \sqrt{( \gamma_{k} \cos\theta)^{2}+ (\phi_{k}
\sin\theta )^{2}}$ in the flux ansatz. Then, the resulting
mean-field free energy is given by
\begin{eqnarray}
&& F_{MF} = \frac{2}{\beta}\sum'_{ks}\ln \sinh\frac{\beta
J\omega_{k}^{s}}{2} \nonumber \\ &&-2NJ\lambda(S+\frac{1}{2})
+\frac{z}{2}NJ\Delta^{2}-\frac{z}{2}NJ\chi^{2} .
\end{eqnarray}

Minimizing $F_{MF}$ with respect to $\Delta$, $\chi$, and
$\lambda$, we obtain self-consistent mean-field equations
\begin{eqnarray}
&& S+1/2 = \frac{1}{N}\sum'_{ks}\frac{\lambda+ s\chi\Theta_{k}}{\omega_{k}^{s}} (n_{k}+1/2) \\
&& \Delta = \frac{1}{N}\sum'_{ks}\frac{z\Delta\gamma_{k}^{2}}{2\omega_{k}^{s}} (n_{k}+1/2) \\
&& \chi = \frac{1}{N}\sum'_{ks}\frac{2zs\Theta_{k}(\lambda+
s\chi\Theta_{k})}{\omega_{k}^{s}} (n_{k}+1/2)   \label{MFE}
\end{eqnarray}
with $\Delta\rightarrow z\Delta/2$ and $\chi\rightarrow z\chi$.

Flux states of our interest are uniform-flux ($\theta=0$) and
$\pi$-flux ($\theta = \pi/4$) phases since they do not break
time-reversal symmetry. \emph{For the uniform phase}, our
numerical analysis shows that the lowest free energy is achieved
by $\Delta=1.1580$ and $\chi=0$. One can easily check that $\chi =
0$ is a solution for the above self-consistent equations in the
uniform-flux case since the right-hand-side of Eq. (17) is odd for
momentum $k$ if $\chi = 0$, thus it vanishes after the momentum
integration, consistent with the left-hand-side of Eq. (17). In
addition, this result is consistent with our physical picture
associated with the sign of the ferromagnetic hopping term.
Schwinger bosons are condensed to the $k^{*}=(0,0)$ state, which
corresponds to the collinear antiferromagnetic order. Staggered
magnetization is found to be $m_{0}=0.3034$, which is the same as
the Auerbach's result\cite{Book}. The ground state energy per bond
is given by
\begin{equation}
E_{0} =  - \Delta^{2} = -0.3352 \label{E0} .
\end{equation}

\emph{For the $\pi$-flux phase}, there are two branches of bosons,
$\omega_{k}^{+}$-boson and $\omega_{k}^{-}$-boson. Spinon
condensation arises in each branch when

\emph{(1) $\lambda= \Delta +\sqrt{2}\chi/2$.} At the wave vector
$k^{*}=(0,0)$ we obtain $\omega^{+}_{k^{*}}>0$ but
$\omega^{-}_{k^{*}}=0$. The self-consistent equation (\ref{MFE})
deduces $\chi=0$ corresponding to the lowest energy, which is the
same as the uniform-flux case, and $\pi$-flux doesn't give any
particular effect. N\'{e}el ordering occurs only for the
$\omega_{k}^{-}$ branch.

\begin{figure}[t]
\begin{center}
\includegraphics[width=8cm]{Dispersion.eps}
\end{center}
\caption{ (Color online) $\omega_{k}^{+2}$ and $\omega_{k}^{-2}$
in the $\pi$-flux phase when $\lambda = \Delta -\sqrt{2}\chi/2$
with $\Delta=1.2021$ and $\chi=0.2349$, where there exists a
contour for the quasiparticle spectrum to cross from positiveness
to negativeness in $\omega_{k}^{-2}$.} \label{fig:Ek_PI}
\end{figure}

\emph{(2) $\lambda = \Delta -\sqrt{2}\chi/2$.}
$\omega_{k}^{+}$-branch bosons are condensed to the $k^{*}=(0,0)$
state, which implies that collinear antiferromagnetic ordering is
also realized within $\omega_{k}^{+}$ bosons. On the other hand,
if we examine the dispersion of low lying excitations of
$\omega_{k}^{-}$ bosons, we find $\omega_{k}^{-} \approx
\sqrt{2}\Delta/2 \left( |k|^{2}-4\sqrt{2}\chi/\Delta\right)^{1/2}$
around the zero point. That is, there is a ring divergence rather
than points provided that $\chi \neq 0$ (see Fig.
\ref{fig:Ek_PI}). Thus, for the $\omega_{k}^{-}$ branch the bosons
with $|k|^{2} \leq 4\sqrt{2}\chi/\Delta$ are all going into the
condensate portion of the boson state. In other words, the density
of $\omega_{k}^{-}$ bosons stays at $|k|^{2} \leq
4\sqrt{2}\chi/\Delta$ in momentum space, thus many kinds of
non-collinear magnetic ordering emerge. Actually, we obtain a
non-zero $\chi=0.2349$ and $\Delta=1.2021$, solving Eq.(\ref{MFE})
numerically. Moreover, comparing with the ground state energy of
the uniform-flux phase Eq.(\ref{E0}), this complex magnetic state
is found to have a lower energy indeed,
\begin{eqnarray}
E_{\pi} = -\Delta^{2}+\chi^{2}= - 0.3578 .
\end{eqnarray}
We can extract the collinear staggered magnetization from the
$\omega_{k}^{+}$ branch, and find $m_{0}=0.1043$. This value is
much smaller than that of the uniform-flux case owing to
enhancement of ferromagnetic correlations.

\subsection{Discussion}

In the previous section we have seen that ferromagnetic
correlations do not contribute to physics of collinear
antiferromagnetism in the conventional Schwinger-boson mean-field
approximation, i.e., uniform-flux ansatz. On the other hand, the
$\pi$-flux phase turns out to be more stable than the uniform-flux
phase, and the emergence of $\pi$-flux enhances ferromagnetic
correlations, causing a complex magnetic state, where there exist
various ordering wave vectors.

Nature of the magnetically ordered state in the $\pi$-flux phase
is an important question. The present semiclassical approach does
not seem to be sufficient for determining the resulting ground
state. This situation reminds us of
"order-by-disorder",\cite{Order_By_Disorder} where quantum
fluctuations split degeneracy and determine its ground state. One
possible scenario in the square lattice is that magnetic ordering
is still to show collinear antiferromagnetism despite the presence
of such "degenerate" states, i.e., many $k^{*}$s corresponding to
ordering vectors, since magnetism measured from the degenerate
states will be cancelled out after momentum integration if the
condensation amplitude at each momentum point is assumed to be the
same as each other. These contributions reduce the strength of the
collinear antiferromagnetism, as seen in the previous calculation.
This is an important effect of ferromagnetic fluctuations in the
antiferromagnetic ground state.

Existence of the complex spin texture prohibits emergence of
gapless U(1) gauge fluctuations owing to nonzero vacuum
expectation values of both spinon-hopping and spinon-pairing order
parameters. Instead, Z$_{2}$ gauge theory appears for possible
non-magnetic phases resulting from this complicated spin
pattern.\cite{Sachdev_Review} Then, deconfined spinon excitations
are expected to appear at high energies beyond their excitation
gap. Actually, dynamic spin-excitation spectra have shown that
there is large spectral weight at high energies beyond the
spin-wave approximation in undoped cuprates.\cite{AF_spinon} In
the present context this unidentified spectral weight may be
identified with deconfined spinon continuum allowed by Z$_{2}$
gauge theory.

However, it should be noted that the Z$_{2}$ gauge structure is
allowed only in the low energy limit, more precisely, $T <
T_{\chi}$, where the ferromagnetic exchange-hopping parameter has
its nonzero expectation value below $T_{\chi}$. Then, U(1) gauge
fluctuations appear above this temperature. The Z$_{2}$-U(1)
crossover makes deconfinement of spinons not clear. This suggests
to measure dynamic spin spectra carefully at high energies as a
function of temperature although it is beyond the scope of the
present mean-field study to predict this temperature accurately.

\section{Doped antiferromagnetic Mott insulator}

\subsection{A slave-fermion mean-field theory of the t-J model}

\subsubsection{A slave-fermion effective action}

We start from the t-J model for doped Mott insulators
\begin{eqnarray} && H = - t \sum_{ij}(c_{i\sigma}^{\dagger}c_{j\sigma} + H.c.)
+ J \sum_{ij}(\vec{S}_{i}\cdot\vec{S}_{j} - \frac{1}{4}n_{i}n_{j})
.  \nonumber \\ \end{eqnarray}
Based on the U(1) slave-fermion representation
\begin{eqnarray} && c_{i\sigma} = \psi_{i}^{\dagger}b_{i\sigma} \end{eqnarray} with the
single occupancy constraint $\sum_{\sigma}
b_{i\sigma}^{\dagger}b_{i\sigma} + \psi_{i}^{\dagger}\psi_{i} =
2S$ where $S$ is a value of spin, here $S = 1/2$, one can rewrite
the spin-exchange term and electron hopping term in terms of
fermionic holon and bosonic spinon operators as follows
\begin{eqnarray}  && J \sum_{ij}(\vec{S}_{i}\cdot\vec{S}_{j} -
\frac{1}{4}n_{i}n_{j}) \nonumber \\ && \rightarrow
\frac{J}{2}\sum_{ij}|\Delta_{ij}^{b}|^{2} -
J\sum_{ij}(\Delta_{ij}^{b\dagger}\epsilon_{\alpha\beta}b_{i\alpha}b_{j\beta}
+ H.c.)  , \nonumber \\
&& - t \sum_{ij}(c_{i\sigma}^{\dagger}c_{j\sigma} + H.c.)
\rightarrow   t\sum_{ij}(\chi_{ji}^{\psi}\chi_{ij}^{b} + H.c.) \nonumber \\
&& - t \sum_{ij}(b_{i\sigma}^{\dagger}\chi_{ij}^{b}b_{j\sigma} +
H.c.) + t \sum_{ij}( \psi_{j}^{\dagger}\chi_{ji}^{\psi}\psi_{i} +
H.c.) , \nonumber \\ \end{eqnarray} where the bond operators
\begin{eqnarray} \Delta_{ij}^{b} = \sum_{\alpha\beta}
\epsilon_{\alpha\beta}b_{i\alpha}b_{j\beta} , ~~~ \chi_{ji}^{\psi}
= \sum_{\sigma} b_{i\sigma}^{\dagger} b_{j\sigma} , ~~~
\chi_{ij}^{b} = \psi_i \psi_j^{\dagger} \nonumber \\ \end{eqnarray}
describe antiferromagnetic, ferromagnetic correlations, and
hopping of doped holes, respectively. Comparing with the
Heisenberg Hamiltonian [Eq. (\ref{AFH})], one can see
$-t\chi_{ij}^{b}$ and $J\Delta_{ij}^{b}$ correspond to $J
\chi_{ij}$ and $J \Delta_{ij}$, respectively.

Using the above expressions, the t-J model in the electron
language is mapped onto exactly the same model but with
fractionalized particles such as spinons and holons in the
following way
\begin{eqnarray} && L_{eff} = \sum_{i}b_{i\sigma}^{\dagger}(\partial_{\tau} -
\mu)b_{i\sigma} - t
\sum_{ij}(b_{i\sigma}^{\dagger}\chi_{ij}^{b}b_{j\sigma} + H.c.)
\nonumber \\ && -
J\sum_{ij}(\Delta_{ij}^{b\dagger}\epsilon_{\alpha\beta}b_{i\alpha}b_{j\beta}
+ H.c.) + \frac{J}{2}\sum_{ij}|\Delta_{ij}^{b}|^{2} \nonumber \\ && +
\sum_{i}\psi_{i}^{\dagger}\partial_{\tau}\psi_{i} + t \sum_{ij}(
\psi_{j}^{\dagger}\chi_{ji}^{\psi}\psi_{i} + H.c.) +
t\sum_{ij}(\chi_{ji}^{\psi}\chi_{ij}^{b} + H.c.) \nonumber \\ && + i
\sum_{i}\lambda_{i}(b_{i\sigma}^{\dagger}b_{i\sigma} +
\psi_{i}^{\dagger}\psi_{i} - 2S) , \end{eqnarray} where $\lambda_{i}$ is a
Lagrange multiplier field to impose the single occupancy
constraint.

It is important to notice that ferromagnetic exchange correlations
in the spin-exchange term is not allowed in the hole-doped case.
This implies that at half-filling, this effective Lagrangian
reduces to the conventional Schwinger-boson theory instead of the
"flux" Schwinger-boson theory since the absence of holons results
in $\chi_{ij}^{b} = 0$, causing ferromagnetic correlations to
vanish, i.e., $\chi_{ij}^{\psi} = 0$. The reason why we do not
introduce the ferromagnetic correlation term from the Heisenberg
term is that when holes are doped, the presence of charge
contribution, $- \frac{1}{4} n_{i} n_{j}$, does not allow the
simple ground-state-energy analysis even for the case of classical
spins, performed in the study of the Heisenberg model, thus it is
not obvious that introduction of such contributions lowers the
ground state energy. Here, we focus on the hopping term of the t-J
model instead, giving rise to ferromagnetic spin correlations
induced by doped holes. This doping-induced
ferromagnetic-correlation term will play an important role in the
structure of magnetic ordering. As seen from its sign, opposite to
the half-filled case, it will contribute even in the uniform-flux
case, and modify the collinear antiferromagnetism drastically.

In the following we will consider the $\pi$-flux phase although we
comment on the uniform-flux case briefly. There are two reasons
for considering such a flux phase. The $\pi$-flux phase is
time-reversal symmetry-preserving, thus physically allowed. More
importantly, the $\pi$-flux ansatz gives rise to four hole
pockets, consistent with the previous studies\cite{SF_OLD}, where
the spinon-holon exchange hopping term (Shraiman-Siggia term) is
taken into account in the context of the perturbation theory,
revealing that holons reside in the four diagonal points. Although
we do not know the connection between our flux-phase result and
the previous perturbation theories, the $\pi$-flux ansatz
reproduces such hole pockets.\cite{Luttinger_Theorem} On the other
hand, the uniform-flux phase does not allow the hole pockets.

\subsubsection{$\pi$-flux ansatz}

\begin{figure}[t]
\begin{center}
\includegraphics[width=8cm]{Ek.eps}
\end{center}
\caption{ (Color online) Energy dispersion of fermionic holes,
where $Min[\xi_{k}^{\psi}]=0$ results at $k=(\pm \pi/2, \pm
\pi/2)$.} \label{fig:Ek}
\end{figure}

Four order parameters are assumed to be as follows for the
mean-field analysis
\begin{eqnarray} && \Delta_{ij}^b \rightarrow \Delta_b , ~~~~~
 i \lambda_{i} \rightarrow \lambda , \nonumber \\ &&
\chi_{ij}^{b} \rightarrow \chi_{b}e^{-i\phi_{ij}^{b}} , ~~~~~
 \chi_{ij}^{\psi} \rightarrow \chi_{\psi}
e^{-i\phi_{ij}^{\psi}} , \end{eqnarray}
decoupling the slave-fermion effective Lagrangian, where the
spin-singlet pairing order parameter and Lagrange multiplier field
are assumed to be uniform and real while the hopping parameters of
spinons and holons have their phase contributions. A nonzero value
of $\Delta_b$ corresponds to short-range antiferromagnetic
correlation as discussed before, and a nonzero $\chi_b$
($\chi_\psi$) implies hole (spinon) mobility or ferromagnetic
correlation, which deforms the spin order in the presence of hole
doping. Together with the $\pi$-flux ansatz
\begin{eqnarray} && \chi_{ij}^{b}\chi_{jk}^{b}\chi_{kl}^{b}\chi_{li}^{b} =
\chi_{b}^{4}e^{- i\sum_{\square}\phi_{ij}^{b}} , \nonumber \\ &&
\chi_{ij}^{\psi}\chi_{jk}^{\psi}\chi_{kl}^{\psi}\chi_{li}^{\psi} =
\chi_{\psi}^{4}e^{- i\sum_{\square}\phi_{ij}^{\psi}} , \nonumber \\ &&
\sum_{\square}\phi_{ij}^{b} = \sum_{\square}\phi_{ij}^{\psi} = \pi
\end{eqnarray}
the free energy can be decomposed into the charge (fermion) and
spin (boson) sectors,

\emph{(1) Fermion sector}

\begin{eqnarray} && F_{\psi} = - \frac{1}{\beta}\sum_{ks}^{'} \ln \Bigl\{2
\cosh\Bigl( \frac{\beta E_{ks}^{\psi}}{2}\Bigr) \Bigr\} \nonumber \\ && +
2t\chi_{\psi}\sum'_{k}\sqrt{(\gamma_{k}\cos\Theta)^{2} +
(\varphi_{k}\sin\Theta)^{2}} \nonumber \\ && = -
\frac{1}{\beta}\sum_{k}^{'} \Bigl[ \ln \Bigl\{2 \cosh\Bigl( \frac{
\beta }{2} [2t\chi_{\psi}\sqrt{(\gamma_{k}\cos\Theta)^{2} +
(\varphi_{k}\sin\Theta)^{2}} \nonumber \\ && + \lambda] \Bigr) \Bigr\} +
\ln \Bigl\{2 \cosh\Bigl( \frac{\beta}{2} [-
2t\chi_{\psi}\sqrt{(\gamma_{k}\cos\Theta)^{2} +
(\varphi_{k}\sin\Theta)^{2}} \nonumber \\ && + \lambda] \Bigr) \Bigr\}
\Bigr] + 2t\chi_{\psi}\sum'_{k}\sqrt{(\gamma_{k}\cos\Theta)^{2} +
(\varphi_{k}\sin\Theta)^{2}} \end{eqnarray}

\emph{(2) Boson sector}

\begin{eqnarray} && F_{B} = \frac{1}{\beta}\sum_{ksl}^{'} \ln
\Bigl\{2\sinh\Bigl(\frac{\beta E_{ksl}^{b}}{2}\Bigr)\Bigr\} \nonumber \\ &&
= \frac{2}{\beta}\sum_{k}^{'} \Bigl[ \ln
\Bigl\{2\sinh\Bigl(\frac{\beta}{2}
\bigl\{\bigl(2t\chi_{b}\sqrt{(\gamma_{k}\cos\Theta)^{2} +
(\varphi_{k}\sin\Theta)^{2}} \nonumber \\ && - \mu + \lambda \bigr)^{2} -
\bigl(4J \Delta_{b}\gamma_{k}\bigr)^{2}\bigr\}^{1/2} \Bigr)\Bigr\}
\nonumber \\ && + \ln \Bigl\{2\sinh\Bigl(\frac{\beta}{2}
\bigl\{\bigl(-2t\chi_{b}\sqrt{(\gamma_{k}\cos\Theta)^{2} +
(\varphi_{k}\sin\Theta)^{2}} \nonumber \\ && - \mu + \lambda\bigr)^{2} -
\bigl(4J \Delta_{b}\gamma_{k}\bigr)^{2}\bigr\}^{1/2} \Bigr)\Bigr\}
\Bigr] , \end{eqnarray}
where
\begin{eqnarray} && \gamma_{k} = \cos k_{x} + \cos k_{y} , ~~~ \varphi_{k} =
\cos k_{x} - \cos k_{y} , ~~~ 4\Theta = \pi . \nonumber \\ \end{eqnarray}
Noted from the energy dispersion $\xi_{k}^{\psi} =
\sqrt{(\gamma_{k}\cos\Theta)^{2} + (\varphi_{k}\sin\Theta)^{2}}$
of fermions (Fig. \ref{fig:Ek}), one can see holes are pocketed
around the diagonal points, ($\pm \pi/2, \pm \pi/2$).

\subsubsection{Self-consistent equations}

In this study we focus on the properties at zero temperature.
Minimizing the free energy with respect to $\Delta_b$, $\chi_b$,
$\chi_{\psi}$, $\lambda$ and $\mu$, we obtain the following
self-consistent equations,

\emph{(1) Fermion sector}
\begin{eqnarray}
 && \delta =  \frac{1}{2N_{L}} \sum_{\xi_{k}^{\psi} \leq - \mu/2t\chi_{\psi}} 1 \label{hole} \\
&& \chi_b =-\frac{1}{4N_{L}} \sum_{\xi_{k}^{\psi}\leq - \mu /2t\chi_{\psi}} \xi_{k}^{\psi} \label{chib}
\end{eqnarray}
Above equations clearly show that holons are most densely located
within the Dirac cones at $k=( \pm \pi/2, \pm \pi/2)$. For small
doping we have $\delta = \frac{1}{2\pi} \left(
\frac{\mu}{2t\chi_{\psi}} \right)$ and $\chi_b = -
\frac{\sqrt{2\pi}}{3} \delta^{3/2}$, as derived in appendix.

\emph{(2) Boson sector}

\begin{eqnarray} &&  \frac{1}{2 N_{L}}\sum'_{k,s=\pm}
\frac{-s\xi_k^{\psi} \bigl(\lambda + 2 s t\chi_{b}\xi_k^{\psi} )}{E^b_s(k)}= \chi_{\psi}  \\
&& \frac{1}{N_{L}}\sum'_{k,s=\pm} \frac{8J\Delta_b
\gamma_{k}^{2}}{E^b_s(k)}  = \Delta_b
\\
&& \frac{1}{N_{L}}\sum'_{k,s=\pm}
\frac{\bigl(2st\chi_{b}\xi_k^{\psi} + \lambda
\bigr)}{E^b_s(k)} = (2S + 1) - \delta
\end{eqnarray}
with the spinon-quasiparticle spectrum $E^b_s (k) = \sqrt{\bigl(2
s t\chi_{b}\xi_k^{\psi} + \lambda \bigr)^{2} - \bigl(4J
\Delta_{b}\gamma_{k}\bigr)^{2}}$. It is clear that these
saddle-point equations are reduced to the conventional
Schwinger-boson mean-field equations in the zero-doping limit
$(\delta \rightarrow 0)$ since $\chi_{b}$ vanishes from Eq. (31)
and $\chi_{\psi}$ disappears accordingly from the summation for $s
= \pm$ in Eq. (32). Hole doping effects reduce the amplitude of an
effective spin from $2S$ to $2S - \delta$, as shown in Eq. (34),
and increase ferromagnetic correlations, as shown in Eq. (32).
Accordingly, antiferromagnetic correlations become weaken, seen
from Eq. (33).

In the mean-field treatment magnetic ordering is described by
condensation of Schwinger bosons. Here, we introduce
$\chi_{BC}^{\psi}$, $\Delta_{BC}^b$ and $n_{BC}$ to describe the
contribution from the $E^b_s(k^*)=0$ states, which are taken into
account separately:

\begin{eqnarray} &&  \frac{1}{2 N_{L}}\sum'_{k,s=\pm} \frac{-s\xi_k^{\psi}
\bigl(\lambda + 2 s t\chi_{b}\xi_k^{\psi} )}{E^b_s(k)} \nonumber \\ && +
\chi^{\psi}_{BC}\sum_{k^*,s=\pm}\frac{-s\xi_{k^*}^{\psi}
\bigl(\lambda
+ 2 s t\chi_{b}\xi_{k^*}^{\psi} )}{\lambda}= \chi_{\psi}  \\
&& \frac{1}{N_{L}}\sum'_{k,s=\pm} \frac{8J\Delta_b
\gamma_{k}^{2}}{E^b_s(k)} + \Delta^b_{BC}\sum_{k^*,s=\pm} \frac{8J\Delta_b
\gamma_{k^*}^{2}}{\lambda} = \Delta_b
\\
&& \frac{1}{N_{L}}\sum'_{k,s=\pm}
\frac{\bigl(2st\chi_{b}\xi_k^{\psi} + \lambda \bigr)}{E^b_s(k)} +
n_{BC} \sum_{k^*,s=\pm}\frac{\bigl( 2st\chi_{b}\xi_{k^*}^{\psi} +
\lambda \bigr )}{\lambda} \nonumber \\ && = (2S + 1) - \delta . \label{s}
\end{eqnarray}
If $E^b_s(k^*)=0$ and $\sum_{k^*,s=\pm}n_{BC}(
2st\chi_{b}\xi_{k^*}^{\psi} + \lambda \bigr )/\lambda$ is finite,
spinons are condensed to the $E^b_s(k^*)=0$ states, and the system
possesses a magnetic long-range order. The ordering wave vector
$k^*$ is determined by $E^b_s(k^*)=0$, and especially, $k^*=(0,0)$
corresponds to long-range anti-ferromagnetic ordering. For
definiteness, we have checked that our treatment of these
mean-field equations recovers the uniform-flux Schwinger-boson
mean-field theory correctly. At half-filling the spinon spectrum
of $E^b_{+}(k) = E^b_{-}(k)$ is gapless at $k=(0,0)$ which ensures
their Bose condensation. Solving Eq. (\ref{s}), we see that the
spontaneous staggered magnetization is given by $\langle S_i^z
\rangle = n_{BC} \approx 0.3$, recovering the half-filled result
completely.

\subsubsection{Phase diagram}

Now, let's consider how the antiferromagnetic long-range order
evolves with doping. Due to the $\pi$-flux order, there are two
types of bosons, $B_{+}$ with energy $-E^b_{+}(k)$ and $B_{-}$
with energy $-E^b_{-}(k)$. Away from half-filling holes are
constrained within the Dirac cones, thus Eq. (\ref{chib}) gives
$\chi_b \leq 0$, which deduces $B^b_{+}$ has lower energy than
$B^b_{-}$ at finite doping, i.e., $-E^b_{+}(k)  < -E^b_{-}(k)$.
When $\lambda=8J\Delta_b + 2 \sqrt{2} t \chi_b$ is satisfied, we
have $E^b_{-}(0)=0$ for $B_{-}$ bosons, thus their Bose
condensation results at the wave vector $k^*=(0,0)$, implying an
antiferromagnetic order. For $B_{+}$ bosons within the same value
of $\lambda$, one can easily check that $1/E^b_{+}(k^*)$ shows
divergence along a ring $k^* \in \{ k | E^b_{+}(k) =0\}$. In other
words, the density of $B_{+}$ spinons resides at large number of
$k^*$ states, thus many kinds of incommensurate magnetic ordering
emerge and such a complex spin configuration deviates from the
collinear antiferromagnetic ordering, similar to the half-filling
case in the mean-field approximation.

With increasing doping and $t$, electrons become more active,
implying that ferromagnetic correlations described by $\chi_b$ and
$\chi_{\psi}$ should also increase. However, the antiferromagnetic
order represented by the condensation amplitude $n_{BC}$ becomes
more suppressed with large $t/J$, which is confirmed by the
numerical results. Furthermore, by numerically solving the
self-consistent equations for given value of $t/J=3$,
Fig.\ref{fig:Phase} exhibits that antiferromagnetic ordering
disappears completely above $\delta_c \approx 0.25$\cite{Spin_Value}
while the spin-singlet order persists up to much larger hole
concentration  ($\Delta_b \neq 0$) away from the antiferromagnetic
order. We identify this intermediate non-magnetic spin-gapped phase
with an anomalous metal, as will be discussed in the next section.

\begin{figure}[t]
\begin{center}
\includegraphics[width=7cm]{NFL.eps}
\end{center}
\caption{ (Color online) Doping dependence of $\Delta_b$ and
$n_{BC}$ with $t/J = 3$.\cite{Spin_Value} In order to clearly show
the tendency, $\Delta_b$ and $n_{BC}$ are scaled with the values
at half-filling. The spin-gapped anomalous metallic phase is
marked as aM.} \label{fig:Phase}
\end{figure}

Compared to the uniform-flux case although not shown in the
present paper, we have qualitatively the same phase diagram. This
originates from the fact that the sign of the ferromagnetic
correlation term is negative opposite to the Heisenberg model,
thus such contributions are energetically favorable even in the
uniform-flux phase. However, the presence of the $\pi$-flux order
enhances ferromagnetic correlations as seen in the study of the
Heisenberg model. As a result, the collinear antiferromagnetic
order is killed more rapidly via hole doping in the $\pi$-flux
phase. We have also examined the role of frustrated hopping
effects, i.e., next-nearest-neighbor hopping terms. Such
frustrated hopping effects modify bare dispersions for spinons and
holons. However, we do not find any qualitative changes in the
phase diagram since the presence of $\pi$-flux dominates over the
band-modification effect.

\subsection{Spin-gapped anomalous metal}

As shown in the phase diagram of Fig. 4, hole doping kills the
antiferromagnetic order and results in a paramagnetic state, where
bosonic spinons are gapped but short-range antiferromagnetic
correlations still remain. We identify this phase with an
anomalous spin-gapped metal since charge excitations carried by
holons are gapless, but spin fluctuations are gapped, thus
exhibiting spin-charge separation.

To understand physics of this anomalous metallic phase, it is
necessary to derive an effective field theory. Considering holons
first, one can expand the holon field as
\begin{eqnarray}  \Psi(x) & = & e^{ik_{1}x}\psi_{1}(x) +
e^{-ik_{1}x}\psi_{\bar{1}}(x) \nonumber \\ & + & e^{ik_{2}x}\psi_{2}(x) +
e^{-ik_{2}x}\psi_{\bar{2}}(x)   \end{eqnarray}
around the diagonal points $k_{1} = (\pi/2,\pi/2)$ and $k_{2} =
(\pi/2,-\pi/2)$, where the holon spectrum is linearized as
\begin{eqnarray} && E_{k}^{\psi} =
2t\chi_{\psi}\sqrt{\cos^2 k_x + \cos^2 k_y }  \approx
v_{\psi}\sqrt{k_{x}^{2} + k_{y}^{2}}   \end{eqnarray}
with its velocity $v_{\psi} = 2t\chi_{\psi}$. The holon spinor is
given by
\begin{eqnarray} && \psi_{1}(x) = \left(\begin{array}{c} \psi_{1e}(x) \\
\psi_{1o}(x) \end{array}
\right) , ~~~~~ \psi_{2}(x) = \left(\begin{array}{c} \psi_{2o}(x) \\
\psi_{2e}(x) \end{array} \right) ,   \end{eqnarray}
where $e$ and $o$ represent even and odd sites, respectively. Such
two-component spinors can be combined to form a single
four-component spinor as
\begin{eqnarray} && \psi(x) = \left(\begin{array}{c} \psi_{1}(x) \\
\psi_{2}(x) \end{array}
\right) = \left(\begin{array}{c} \psi_{1e}(x) \\ \psi_{1o}(x) \\
\psi_{2o}(x) \\ \psi_{2e}(x) \end{array} \right) . \end{eqnarray}

An important point is that U(1) gauge fluctuations become gapped
due to condensation of a "charge" $2$ scalar field, here the
ferromagnetic hopping parameter, reduced to gapped Z$_{2}$ gauge
fields, as discussed previously. In other words, hole doping
causes magnetic frustration effects, giving rise to ferromagnetic
correlations. This reduces the emergent U(1) gauge structure down
to Z$_{2}$. As a result, we find the following effective field
theory for the anomalous Z$_{2}$ spin-gapped metal phase
\begin{eqnarray} && {\cal L}_{\psi} = \bar{\psi} \gamma_{\mu}(\partial_{\mu} -
iA_{\mu})\psi - \mu_{r} \bar{\psi}\gamma_{0}\psi , \end{eqnarray}
where Dirac gamma matrices satisfying the Clifford algebra
$[\gamma_{\mu},\gamma_{\nu}]_{+} = 2\delta_{\mu\nu}$ are given
by\cite{Don_Kim}
\begin{eqnarray} && \gamma_{0} = \left(\begin{array}{cc} \sigma_{3} & 0 \\
0 & - \sigma_{3} \end{array} \right) , ~ \gamma_{1} = \left(\begin{array}{cc} \sigma_{2} & 0 \\
0 & - \sigma_{2} \end{array} \right) , ~ \gamma_{2} = \left(\begin{array}{cc} \sigma_{1} & 0 \\
0 & - \sigma_{1} \end{array} \right)  , \nonumber \end{eqnarray}
and $\mu_{r}$ is a renormalized chemical potential associated with
hole doping. $A_{\mu}$ is an electromagnetic field. Note that
gapped spinon excitations are ignored for low energy physics of
this metallic phase. Then, Eq. (42) is our effective field theory
for the anomalous metallic state.

An immediate question is about the transport property in this
metallic phase. Since there is no scattering mechanism with
gapless gauge fluctuations in the above effective field theory,
Fermi liquid behavior is expected to appear in the low temperature
limit, i.e., $\delta \rho(T) = \rho(T) - \rho(T=0) \sim T^{2}$
with resistivity $\rho(T)$. Although this is true in the present
description actually, such a Fermi liquid behavior in transport is
not a full story.

As discussed in the Heisenberg model, there is an energy scale
$T_{\chi}$ associated with the crossover behavior from Z$_{2}$ to
U(1) since ferromagnetic contributions are nonzero below this
temperature. Although we cannot determine this temperature
satisfactorily in our mean-field analysis, gapless U(1) gauge
fluctuations should arise above this crossover temperature. Then,
scattering with such gapless gauge excitations would lead to
non-Fermi liquid physics in this regime. Frankly speaking, there
are various regimes at finite temperatures, associated with not
only the Z$_{2}$-U(1) crossover temperature but also so called the
spin-gap temperature $T_{b}$, where bosonic spinons are
effectively critical above this temperature. $T_{b}$ should not be
confused with $T_{\Delta}$, where spinon-singlet pairing order
appears below this temperature, much larger than the spin-gap
temperature $T_{b}$. In this respect we should consider both
energy scales, and classify various finite temperature regimes. In
the present paper we discuss only low energy physics of this
metallic phase.

\section{Discussion and summary}

\subsection{Coherent electron quasiparticle excitations near the
diagonal points}

The present slave-fermion mean-field description cannot explain
the emergence of sharply defined electron quasiparticles near the
diagonal points and their Fermi liquid behavior because electrons
decay into spinons and holons in the Z$_{2}$ anomalous metal
phase.\cite{ARPES} This is the main criticism in this kind of
decomposition approach if one tries to connect the spin-charge
separation scenario with pseudogap physics of high T$_c$ cuprates.
However, if we consider the regime of $T > T_{\chi}$, the
situation is not perfectly clear owing to the presence of gapless
gauge fluctuations beyond the mean-field description since such
gauge fluctuations cause attractive interactions between holons
and spinons, binding them, which may allow a resonance state
corresponding to an electron-like excitation although it differs
from confinement. Actually, this was a little bit demonstrated,
where noncompact gauge fluctuations give rise to attractive
interactions between "particle" and "hole" (holon and spinon in
the electron spectrum), increasing coherence.\cite{Nodal_electron}
We should confess that this argument is far from consensus even in
the qualitative point of view.

In the low temperature regime, more precisely in the zero
temperature limit where we have studied in this paper, the
situation becomes worse because even gapless U(1) gauge
fluctuations do not exist owing to the gauge-symmetry reduction.
However, we argue that such an electron excitation may still
appear as a resonance state between a spinon and holon. To see
this resonance state, we revisit the hopping-t term in the
slave-fermion representation of the t-J model. We rewrite the
hopping term as follows
\begin{eqnarray} && - t
\sum_{ij}(b_{i\sigma}^{\dagger}f_{i}f_{j}^{\dagger}b_{j\sigma} +
H.c.) \rightarrow t \sum_{ij}(c_{i\sigma}^{\dagger}c_{j\sigma} +
H.c.) \nonumber \\ && - t \sum_{ij}(c_{i\sigma}^{\dagger}
f_{j}^{\dagger}b_{j\sigma} + H.c.) - t
\sum_{ij}(b_{i\sigma}^{\dagger}f_{i}c_{j\sigma} + H.c.) \nonumber \\ && +
t\sum_{ij}(\chi_{ji}^{\psi}\chi_{ij}^{b} + H.c.) - t
\sum_{ij}(b_{i\sigma}^{\dagger}\chi_{ij}^{b}b_{j\sigma} + H.c.)
\nonumber \\ && + t \sum_{ij}( \psi_{j}^{\dagger}\chi_{ji}^{\psi}\psi_{i} +
H.c.) . \end{eqnarray}
It should be noted that the electron operator $c_{i\sigma}$ is
different from the original one since it is a Hubbard-Stratonovich
field although it is a fermion. Rather, it should be understood as
a collective fermionic excitation in the spinon-holon liquid. We
identify this fermion field as an electron, which is expected to
be seen in the low energy regime. Note that hopping of such low
energy electrons is frustrated, viewed from its sign.

The electron-spinon-holon exchange term reminds us of the
slave-fermion representation of the Anderson lattice model, where
localized spins are represented in slave-fermions.\cite{SF_ALM} To
find a self-energy correction from this "hybridization" coupling
seems to be an interesting and important problem since the
spin-charge separation scenario may explain the coherent nodal
electron excitations.

\subsection{d-wave superconductivity}

Another interesting subject is how to describe d-wave
superconductivity in this context. Considering the slave-boson
case, one may regard this study as a straightforward job. In the
slave-boson theory condensation of bosonic holons results in
superconductivity in the presence of spinon singlet pairing since
they form Cooper pairs. However, this structure cannot be applied
to the slave-fermion context. Fist of all, charged holons are
fermionic, thus their condensation is forbidden. Then, the next
choice will be pairing of such fermionic holons. Actually, such
pairing interactions are usually attributed to the presence of
gapless U(1) gauge fluctuations since they cause attractive
interactions between holons living in different sublattices. What
we would like to do is to construct a mean-field theory for such
pairing order from the microscopic model itself. However, if we
start from the t-J model, such an attractive pairing interaction
channel is difficult to find since the exchange term is
represented only in the bosonic-spinon language owing to the
single occupancy constraint, analogous to the fact that the J term
is also expressed in terms of only fermionic spinons in the
slave-boson context.

To avoid this difficulty, we start from so called BCS-Hubbard
model\cite{BCS_Hubbard_SR}
\begin{eqnarray} && H = - t \sum_{ij}(c_{i\sigma}^{\dagger}c_{j\sigma} + H.c.)
-
\sum_{ij}(\Delta_{ij}^{\dagger}\epsilon_{\alpha\beta}c_{i\alpha}c_{j\beta}
+ H.c.) \nonumber \\ && + \frac{1}{g}\sum_{ij}|\Delta_{ij}|^{2} + U
\sum_{i}n_{i\uparrow}n_{i\downarrow} \end{eqnarray}
where the Hubbard-Stratonovich transformation for the Cooper
channel is performed before the constraint is applied. This model
has its own interest in the fact that we can investigate what
happens in BCS superconductivity, increasing local interactions
$U$. Our strategy is that such strong correlation effects are
introduced using the slave-fermion representation in the large-$U$
limit. Then, the pairing term is expressed in the slave-fermion
representation as
\begin{eqnarray} && -
\sum_{ij}(\Delta_{ij}^{\dagger}\epsilon_{\alpha\beta}c_{i\alpha}c_{j\beta}
+ H.c.) \nonumber \\ && = -
\sum_{ij}(\Delta_{ij}^{\dagger}\epsilon_{\alpha\beta}b_{i\alpha}b_{j\beta}
\psi_{i}^{\dagger}\psi_{j}^{\dagger} + H.c.) \nonumber \\ && \rightarrow
\sum_{ij}(\Delta_{ij}^{\dagger}\Delta_{ij}^{\psi}\Delta_{ij}^{b\dagger}
+ H.c.)  - \sum_{ij}(\Delta_{ij}^{\dagger} \Delta_{ij}^{b\dagger}
\epsilon_{\alpha\beta}b_{i\alpha}b_{j\beta} + H.c.) \nonumber \\ && -
\sum_{ij} (\Delta_{ij}^{\dagger}\Delta_{ij}^{\psi}
\psi_{i}^{\dagger}\psi_{j}^{\dagger} + H.c.) ,  \end{eqnarray}
where pairing interactions are renormalized due to Hubbard
interactions. Replacing $\Delta_{ij}^{\dagger}
\Delta_{ij}^{b\dagger}$ and
$\Delta_{ij}^{\dagger}\Delta_{ij}^{\psi}$ with $\Delta_{ij}^{b}$
and $\Delta_{ij}^{\psi}$, respectively, we find the slave-fermion
effective Lagrangian for the BCS-Hubbard model in the large-$U$
limit
\begin{eqnarray} && L_{eff} = \sum_{i}b_{i\sigma}^{\dagger}(\partial_{\tau} -
\mu)b_{i\sigma} - t
\sum_{ij}(b_{i\sigma}^{\dagger}\chi_{ij}^{b}b_{j\sigma} + H.c.)
\nonumber \\ && - \sum_{ij}(\Delta_{ij}^{b\dagger}
\epsilon_{\alpha\beta}b_{i\alpha}b_{j\beta} + H.c.) \nonumber \\ && +
\sum_{i}\psi_{i}^{\dagger}\partial_{\tau}\psi_{i} + t \sum_{ij}(
\psi_{j}^{\dagger}\chi_{ji}^{\psi}\psi_{i} + H.c.) \nonumber \\ && -
\sum_{ij} (\Delta_{ij}^{\psi} \psi_{i}^{\dagger}\psi_{j}^{\dagger}
+ H.c.) \nonumber \\ && +
\sum_{ij}(\frac{\Delta_{ij}^{\psi\dagger}\Delta_{ij}^{b\dagger}}{\Delta_{ij}}
+ H.c. + \frac{1}{g} |\Delta_{ij}|^{2}) +
t\sum_{ij}(\chi_{ji}^{\psi}\chi_{ij}^{b} + H.c.) \nonumber \\ && + i
\sum_{i}\lambda_{i}(b_{i\sigma}^{\dagger}b_{i\sigma} +
\psi_{i}^{\dagger}\psi_{i} - 1) . \end{eqnarray}

Although investigation of this effective Lagrangian is beyond the
scope of this paper, one can read an important aspect of this
Lagrangian immediately. An observed dome-shaped superconductivity
line is expected to appear since $\Delta_{ij}^{b}$ vanishes in the
zero doping limit owing the absence of doped holes, causing
$\Delta_{ij}^{\psi} = 0$ while $\Delta_{ij}^{\psi}$ disappears at
large doping, killing $\Delta_{ij}^{b}$.

\subsection{Summary}

In this paper we have considered dynamics of doped holes in the
antiferromagnetically correlated spin background. The point is
that doped holes frustrate the collinear antiferromagnetic spin
configuration, resulting in more complex spiral-like spin
patterns. This reduces the U(1) gauge symmetry down to Z$_{2}$,
thus the effective field theory appears to be a Z$_{2}$ gauge
theory instead of U(1) in the low energy limit. As a result,
deconfinement of spinons and holons is naturally allowed in
$(2+1)D$. When spinons become gapped via further hole doping, an
anomalous metallic phase results with spin-charge separation. We
argued that there is a crossover energy scale $T_{\chi}$ from
Z$_{2}$ to U(1) above this temperature, where transport should be
more carefully studied in the presence of such gauge interactions.
We also discussed how coherent electron excitations near the
diagonal points can appear in the slave-fermion context. Lastly,
we have speculated superconductivity within the slave-fermion
representation.

redpajama_set_name: RedPajamaArXiv


Senior Night vs. Bethlehem Tuesday, October 23.
On Tuesday evening October 23rd the Shenendehowa plainsmen will be hosting the Bethlehem Eagles for what's to be expected an end of season battle. Come and support the seniors as they take their home court for the final time during regular season play.


text:
Site Inspection: Pittsburgh Bridges Past and Future
Forget everything you thought you knew about Pittsburgh. It has built a reputation as a green, innovative city where the scenic views include the twinkling lights of drone researchers, rather than smokestacks. Gone are the steel mills and, thanks to home-grown talent coming out of University of Pittsburgh, Indiana University and Carnegie Mellon University, along with 66 other public and private institutions, the city is now home to Google, Apple, Uber and Facebook offices working on everything from robotics to self-driving cars.
Pittsburgh International Airport (PIT) averages 414 flights per day to 74 destinations and is breaking ground on a $1.1 billion modernization that will actually shrink the size of the terminals, making it easier to navigate and opening up space for improved security and parking.
Meet and Sleep
David L. Lawrence Convention Center features 1.5 million sq. ft. of LEED Platinum-certified meeting and exhibit space with sweeping river views and 1,300 sq. ft. of outdoor gardens that grow ingredients for the hyper-locally sourced catering menu. This modern facility is steps from The Westin Convention Center, Pittsburgh and its 38,464 sq. ft. of event space and 616 guest rooms.
The city's newest convention hotel, AC Hotel Pittsburgh Downtown offers access to Market Square and the Cultural District and almost 3,000 sq. ft. of event space, along with 134 guest rooms. Nearby, Kimpton Hotel Monaco Pittsburgh is a pop of color in a 1903 Beaux Arts-style building with more than 11,300 sq. ft. of event space, including a two-story ballroom and rooftop suite for view-infused VIP gatherings.
Nearby, Omni William Penn Hotel boasts 52,000 sq. ft. of meeting space in an elegant, historic building with a basement speakeasy lounge. For something completely different, Drury Plaza Hotel Pittsburgh Downtown is the spot if you want to plan a meeting in an old bank vault. The art deco building was The Federal Reserve Bank of Pittsburgh and now takes deposits on more than 200 guest rooms and 10,000 sq. ft. of event space.
It wouldn't be a trip to Pittsburgh without a Primanti Bros. sandwich stuffed full of meat, coleslaw and French fries, but the culinary scene has evolved from the days when truck drivers needed something they could hold in one hand as they made their way from the Strip District (no, not that kind of district—it just refers to the strip of land where the warehouses fronted the river). Whether your group opts for a 'Burgh Bits and Bites Food Tour or navigates its own way through Zagat's 2015 No. 1 Food City in the United States, you will find James Beard-nominated chefs and creative takes on the diverse ethnic cuisine residents have been cooking for generations. Check out Smallman Galley, a 200-seat food hall that allows multiple chefs to test their inventive culinary concepts.
The city's lounges have also come a long way since it played a pivotal role in 1794's Whiskey Rebellion. And the libations in that boilermaker aka "a shot and a beer" are probably craft brews from one of the 30 members of Pittsburgh Brewers Guild.
Pittsburgh is still a sports town. New residents are issued a yellow Terrible Towel to cheer on the beloved Steelers at Heinz Field stadium. Across the river, PPG Paints Arena is home to the NHL Pittsburgh Penguins. Both are creative, only-in-Pittsburgh meeting and event locations.
Another claim to fame for this diverse city is memorialized in Andy Warhol Museum, where the King of Pop Art's evolution fills seven floors.
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redpajama_set_name: RedPajamaCommonCrawl


Houston — US weekly coal production was estimated to be 10.5 million st for the week ended March 30, down 6.6% from the previous week and down 26.3% from the year-ago week, US Energy Information Administration data showed Thursday.
This was the fifth week in a row of decreases from the year-ago week, and was the largest year-on-year drop since the final week of 2017, when output fell 28.2%.
Across the board, the four major basins dropped week on week and year on year, experiencing their lowest production levels in the first quarter of the year.
From the five-year average of almost 16 million st produced in the thirteenth week of the year, 2019 production was at a deficit of 34%.
In Q1, coal production fell 3.8% from the previous year.
Production in Wyoming and Montana, largely made up of Powder River Basin coal, dropped the most from the year-ago week, down 29.1% with output of over 4.6 million st. From the previous week, production dropped 6.5%. On an annualized basis, production from the two states would be over 306 million st, down 9.9% from 2018 output.
Central Appalachian production followed with total output of about 1.4 million st, down 26.1% from the corresponding week last year and down 9.5% week on week. CAPP output on an annualized basis would total 93.6 million st, down 2% from 2018 production.
Illinois Basin production came next, down 24.6% year over year, with almost 1.6 million st. Production fell 3.2% on week. Annualized IB production would total over 100 million st, down 4.5% from last year's production.
Northern Appalachian output totaled 1.5 million st, down 22.9% from the year-ago week and down 4.4% from the previous week. Annualized NAPP production would be 97.7 million st, down 5% from the previous year's output.
In Q1, total US production was over 173 million st. Annualized US production comes to about 694 million st, down 7.6% from 2018 output.
S&P Global Platts Insight magazine showcases our pricing, news and analytics across global energy and commodities markets.


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A Sit Down With South African Artist: CeeBoo And Her Debut Album "Breaking Dawn"
Written by James Hall, My House Radio 8/18/2019
Who is CeeBoo??
She was christened Sibusiso Msesiwe and now has donned the moniker CeeBoo and is brimful with flair and creativity in her latest offering City Rain Remix originally done by DJ Mobi Dixon featuring Mque.
CeeBoo is a versatile cross over artists whose lilting and honey raw voices wafts swiftly between Afro-soul and R&B. Born and raised in the coastal town of East London, she started singing at the tender age of six, as part of her church choir and went on to learn to play the piano on her own.
"I am a self-taught musician. I enjoyed learning a skill without conscious awareness of the underlying processes of what is being learned. In the process of curiosity you make mistakes, learn and grow because you have no scope or boundary to limit you. It is for this reason that I do not like being boxed as a musician" explained CeeBoo.
CeeBoo's musical journey from the church in later years migrated to poetry where she raided open mic sessions. Later, she would turn the poems into songs about her lived experience and things that she imagined. "The poetry sessions gave me the platform and confidence to be able to bare my soul in front of a live audience to examine what I had to offer artistically. When I turned to music my soul just soared, backed by the confidence that I was in full control expressing my art" chimed CeeBoo.
In 2010 as part of Elements of Soul, a touring venture which she wrote and produced the music, toured South Africa and Namibia. Their album was called Music in Me and helped profile her musical prowess. The musical odyssey culminated with Breaking Dawn her solo debut album.
● Was the lead vocalist of a group called Elements Of Soul and they released an album in 2011.
● Performed alongside the likes of Queens Of Dance, Bantu Soul, Top Mafia, DJ Menace (Beyonce Records), DJ Clock (AMPM), Master Wakes of Kalawa Jazzme Dance, Mwezi Zazi, Msaki and Zama Ntshona.
● Performed on Etv's Sunrise and Club808.
● BEAT Magazine Awards as the Best Female Vocalist Nominee in 3 categories.
● Used to perform on Thursday Nights at Kulcha Noir, an upmarket Johannesburg restaurant,
● Performed and Toured in Windhoek Namibia alongside Speedy (Bongo Muffin) and several other artists.
● Performed at BCMM Switching on of the Festive Lights 3 years in a row, having been an opening act for Winnie Khumalo and Micasa.
● She recorded her solo album in 2013.
● Performed at several corporate functions in and around East London.
● Performed at the Launch of the 1st English/Xhosa Dictionary in 2014
● Performed at the Bingo Royale Casino as the first Resident Artist in 2014
● Hosted a Live Music Show at the Guild Theatre (East London), in 2014
● Performed for the Eastern Cape Premier at an event for the Official Pronouncement of the Audit Outcome in 2016
● Performed at the Buyel' Ekhaya Music Festival in 2016 ● Performed at the 2017 State Of The Metro Address
● Performed at the 2018 BCMM Women Nomination Awards
● Collaborated with DJ Clock (The Founder of AM-PM Productions), Bantu Soul, Master Wakes (of Kalawa JazzMe Records) and Nkanyiso Bengu (of Joyous Celebration).
● Was a part of a Talent Search and Produced Songs for local artists from Ntabankulu.
● Was recently invited to perform at the 2019 New Orleans Jazz Festival and to attend Educational Workshops, where she would be doing Motivational Speaking as well.
● Does Motivational Speaking at underprivileged schools in and around East London.
● Performed at the 2019 UMTIZA ARTS FESTIVAL.
● Recently released her debut album – Breaking Dawn, (Available on all Digital Music Platforms).
CeeBoo
Q: It truly is a pleasure! It seems like you have come out of nowhere! how are you feeling right now with so much attention on you?
Hahaha, I feel like I can take over the world with my voice right now. Like the universe is my playground. Like a kid in a candy store, with a personality so vibrant to contain. I'd say the world is ready for me now and I'm definitely ready for the world!
Q: So where are you from? I like the name Cee Boo what does it mean?
I was born and bred in East London, a city in the Eastern Cape and in South Africa. The name CeeBoo is derived from my original name, which is a unisex name that confuses people at times, LOL. My birth name, Sibusiso, means Blessing and is taken from the Zulu language. So CeeBoo is a short version of the first 4 letters in my original name. It is Uniquely spelled this way, to assist my followers in pronouncing it easier.
Q: When did you start writing/producing music – and what or who inspired you?
I started writing poems that I turned into songs. I literally woke up one morning, when I was 6 years of age, and I started playing the keyboard/piano, composed music, sang my poems and I just never looked back. I was inspired by my own personal experiences. Growing up, childhood memories, good and bad, the pain from my past inspired me too. Birds inspire me, Books, Music, People of Good morals and values. But the people who inspire me the most : (1) My only surviving parent – Reverend Owen, (My Dad). (2) My kids and (3) My husband and manager: Mr. Denzil Celin Gounden.
Q: You seem to pull in musical styles from Afro house to R & B on your new Album which is great by the way. What influenced it?
I'm a non-conformist. I don't Lead by Following. My musical inclination allows me to go beyond unforeseen and unknown boundaries. And because Music, to me is a Natural Gift, you will find me in almost every genre. That is what inspired my debut album – Breaking Dawn.
Q: So I'm really loving the hit house track: Azange Ndambona what is the song about?
Azange Ndambona means: " I've never seen someone like this before. Someone so kind, so genuine and so true." This song is way ahead of its time, as it is a proven prophecy. I wrote this song and asked my late mom for her blessings and advice, in my current relationship and marital union. And she peacefully passed on, after saying Yes and giving us her blessings to marry and settle down.
http://myhouseradio.fm/wp-content/uploads/2019/08/Azange-Ndambona.mp3
Q: So what label are you currently under? or are you an independent Artist.
I am an independent artist, under No Label.
Q: I saw that just this summer, you played a few shows and are all over the radio, any future plans you'd like fans to know about?
That's a great question!!! I'd love to do a World Tour. So that I can fully engage, embrace and inspire the Masses, as they do to me.
I want to be out there in the Universe, spreading Positive messages through music and song. To get my Brand known and to remind others that life is not so bad. As I am a living testimony to that.
Q: Do you have any future collaborations coming up or anyone you'd like to work with?
There are far too many Legends and Undiscovered Geniuses to mention. My life – long dream is to share a stage with Patti LaBelle, Anita Baker, Alicia Keys and Swizz Beats, Angie Stone, The Weekend, Pharrell, Angie Stone, Jill Scott, Erykah Badu, Lauren Hill and to have an album produced by Quincy Jones, Babyface, Darkchild and Timberland to mention a few. I'd also like to feature on songs with some of my newly made Facebook Friends, DJs, and Producers across the Globe.
Q: So I ask every new artist on the scene about staying power where do you see yourself in the future?
I see myself empowering and nurturing our up and coming artists. The new generation of music, to guide them and share everything I know. The best thing to do is to educate and disseminate Positive energy, Powerful knowledge, and Valuable Resources to kids in broken homes, underprivileged communities and to motivate our Youth. Giving them Music to hold on to and focus on. Shifts and reduces the pressures of life on the dark side of our existence on Earth. Example: Criminal Activities, Teenage Pregnancies, Gangsterism, Peer Pressure, Alcohol, and Drug Abuse, etc. So I'd like to open up a music academy, to harness these souls and talents. Because I just love what I do and helping someone else, is always so refreshing and rewarding. It brings my heart Pure Joy at the end of every day.
Q: Lastly I'd like to say thank you for sitting down with us here at My House Radio. I see great things for you in the future.
Once again, I'd like to thank you very much for taking this time to get to know me and introducing me to the Masses. I do hope that I can come to perform and visit your country soon! I trust you will enjoy Breaking Dawn and let's dance again on MyHouse Radio!
CeeBoo's New Album Is Available on 6 digital platforms, here are 3 Links as guides.
Or you can Simply Type and Search "CeeBoo'.
https://open.spotify.com/album/37Oc3 mXMOz9HUxKnw9yvxY
https://www.deezer.com/album/982127 72
https://music.apple.com/us/album/brea king- dawn/1465454569?uo=4&app=music& at=1001lry3&ct=dashboard&app=itune s&at=1001lry3&ct=dashboard
For bookings
My Number Is : 081 594 0900 – CeeBoo
My Managers' Number Is: 081 484 5656 – Mr Denzil Celin Gounden
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By J Hall|2019-08-18T21:41:41+00:00August 18th, 2019|Announcements, International, Music News, My House Radio, New Release, Uncategorized|0 Comments
About the Author: J Hall


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Batman's Decline From Hero to Just Another Angsty White Guy
Author: Brian RafteryBrian Raftery
The first time I saw a grown-up get angry about a comic book movie was in the summer of 1988, at a sci-fi convention outside of Philadelphia. I was 12 years old, and, as such, was wearing a Batman hat. A lumpy vendor-slash-Alex Karras-replicant saw me digging through his back issues, and headed in my direction. Soon he was standing over me, his arms folded firm, his grimace held tight.
"Did you hear who they picked to play him?," he asked. "Michael Keaton! The guy from Mr. Mom is gonna be Batman!" With that, he shook his head and stared at the ground, looking as though he was going to spit on the unsold back-issues of Rom: Space Knight piled underneath. A few feet away, another dealer shrugged and exhaled dramatically, a show of chagrined solidarity.
Fans knew we were in the midst of a creatively gilded age, a time when the medium's ambitions and visibility were reaching an intertwined, mutually nurturing apex. Only one person could screw it up now: Batman.
Their reaction may have been a little extreme, but it's hard to fault them too much, as by the late '80s, we comic book lovers were on the defensive. For months, a masked vigilante had been tracking us down and taking us out, one by one, in a past-rectifying attempt to—wait, sorry. That's actually the plot of Watchmen. The real-ish threat facing fans was far less lethal, but worrisome nonetheless, especially since things were going so well for us: After decades of barely being taken kinda-seriously, comic books were finally inching closer to mainstream acceptance, perhaps even semi-coolness. They were weightier, darker, and more vividly executed than ever before, and they'd even festooned themselves with a new descriptor—the hilariously hoity-toity "graphic novel"—that, in retrospect, was the desperate-image-makeover equivalent of a freshman English major tattooing "Franny" and "Zooey" on his or her knuckles.
And while there were still plenty of cruddy titles (Secret Wars II, for example, was the Stayin' Alive of Marvel sequels), fans knew we were in the midst of a creatively gilded age, a time when the medium's ambitions and visibility were reaching an intertwined, mutually nurturing apex. Only one person could screw it up now: Batman.
Michael Keaton as Batman: 1988's Concerned Nerd Talking Point No. 1
Specifically, Keaton's pending version of Batman, the hottest topic of a discussion that rang through specialty shops, convention centers, and summer-camp pow-wows. Debating the merits of superheros (and superhero movies) may now be the fossil fuel for much of the modern internet, but trust me, we were just as obsessed with this stuff in the pre-dial-up era; you would not believe how many sleepovers devolved into parliamentary debates on the relative suckiness of Alpha Flight.
Batman, though, was that year's Concerned Nerd Talking Point No. 1. The character had recently undergone an astonishingly dark rewrite, one that had begun with Frank Miller's Batman: The Dark Knight Returns, the future-set 1986 series that depicted its hero as a bitter retiree who returns to Gotham City to put down gangs of punks and eventually tries to take out Superman. Then came 1987's Batman: Year One, Miller's only slightly less grim retelling of the Caped Crusader's origin; 1988's The Killing Joke, an Alan Moore one-shot that deepened (and popularized) the Joker's psychotic tendencies; and then, finally, Batman: A Death in the Family, a headline-making stunt for which readers were invited to spend 50 cents to call a 1-900 number and decide whether Robin lived or died (he died). Batman was never the peppiest character in the DC universe, but by the end of the '80s, he could have won a frown-off against Peter Murphy.
With the on-the-stands Batman now so thoroughly gritty, the worry was that Keaton—a stand-up turned comedy star—would revert the character to his way more brightly lit (and, in some fans' eyes, far dimmer) TV-version roots. In that incarnation, Adam West's Batman (dry and mighty) and Burt Ward's Robin (spry and stupid) fought cartoonish-even-for-a-comic book villains, and got caught up in a never-ending series of astonishingly ill-planned traps. I loved West's Batman: He was noble, even-keeled, and resourceful enough to carry around shark-repellant Bat Spray at all times (he also had that catnippy bubblegum-boogie theme song, with its nah-nah-nah-nah mantra). But I also recognized the show as kids' stuff, and espoused the virtues of the bummed-out, vengeance-seeking Batman to any sneering kid (or patient adult) who listened.
We got our way. But in the process, Batman may have lost his.
For most non-diehards, though, the memory of the campy Batman was impossible to forget. The series had been off the air since 1968, yet thanks to reruns the show persisted as the media's main reference point for not just Batman, but for comic book culture in general. Every "comics are for adults now!" article featured some lame Zap! Boom! Pow! reference (a sure sign you were reading an article written by a fusty square). If Keaton's Batman was going to try to be funny, we believed, comic books would lose their still-fragile cachet. So we huddled harrumphed during our back-of-the-comic-shop chop-it-ups, and prayed that Hollywood would deliver the darkest, dourest, most integrity-edifying big-screen version of Batman possible.
A Billion Ways to Be the Bat
Because no one's allowed to write about Batman movies on the Internet without first establishing their superhero bona fides—look it up; it's buried deep in the Affordable Care act—I should confess that my comic book cred is shaky. My primo obsessive years started in 1983, when I purchased Marvel's adaptation of *Krull * from a Manhattan newsstand, and lasted until around the summer of 1990, when the first issue of Todd McFarlane's new Spider-Man was launched amid a sad blast of hoopla and collector-baiting special-edition nonsense that even I, as a Stan Lee-loving teenager, found dispiriting. So I checked out. I've since dipped back into the comics world—and how can you not, in an era of Paper Girls, Sex Criminals, Saga, Ms. Marvel, and the like?—but the gaps in my knowledge are bigger than a Snark ship (that's a deep-cut Power Pack reference for all the Simonson/Brigman-heads out there).
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Yet throughout the height of my comic love, there was no character I followed more closely than Batman, whose exploits I revisited whenever I could. I still have my original paperback copy of The Dark Knight Returns; it looks like it's been through the gentlest of wood-chippers (the same goes for my editions of Year One and The Killing Joke). I can recall blood-spattered panels from the brutal 1988 mini-series Batman: The Cult—some of which gave me nightmares—with ease. I spent at least 10 bucks voting for Robin's death.
And every time I've wandered into a comics shop in recent years, or gone down a conversational batcave with a comics-following friend, I've wound up exploring (and loving) modern Batman stories like Scott Snyder's Batman: Black Mirror and The Court of Owls, or Ed Brubaker and Greg Rucka's cop-procedural Gotham Central. I'm still drawn to the character, even if I can't follow the Bat-signal as closely as I once did.
For the most part, the Batman stories I loved adhere to the enjoyably downbeat vision of Batman that's made him a pop-cultural fixture for more than 75 years: That of a loner detective, haunted by his past and taunted by his foes, who commits fully to whatever definitions of justice and mercy he tends to be into at that point (in his early years, Batman had seemingly no problem with killing off bad guys, though by the early '80s, he was more likely to drop them off at Arkham Asylum). And while I admired the character's toughness, I also dug his nifty accouterments (Giant pennies! A dinosaur!) and the fact that, unlike Superman or Wonder Woman, he was a superhero without any special powers. If you'd asked me when I was 11 or 12 what job I wanted to when I got older, I would have replied "guy who gets to read a lot about Batman." But the more honest answer would have been: "Batman."
The Best Bat-Manifestation Yet
So I was surprised and relieved when I finally saw Tim Burton's Batman on opening night on June 23, 1989. Have you watched that movie lately? Even if you never cared about comic books, it's a deeply dippy delight: An over-budgeted, studio-spawned oddity that somehow seems both painstakingly thought-out and completely made up on the spot. There are scenes so goofy, you can just imagine Burton and Jack Nicholson—two guys who no doubt shared an almost clinical disdain of big-business execs—wondering, "How should we fuck with the suits today? I know: What if you punched out a TV and yelled about enemas while dressed like Grape Ape's pimp?"
But while Burton's film has to-the-core elements of the glower-tripping Batman we fans were hoping for—the goth-deco architecture, the baroque mutilations, and an ending that ultimately plays as a downer, no matter what song you put in the end credits—its biggest asset was Keaton. In both Batman and 1992's Batman Returns, Keaton plays Batman (and, more importantly, Bruce Wayne) as daffy, detached, and slightly bemused by his own predicament; it's as though the actor just waltzed in from the set of a screwball comedy he was filming a few soundstages away. When he's out of costume, Keaton's eyebrows aim skyward like quizzical cathedrals, and his mouth flashes unexpectedly to a strange half-smile. There's torment within Keaton's Batman, to be sure, and a barely tempered anger, yet as troubled as he is, the world doesn't weigh on his shoulders; it just kind of hovers there.
Keaton's take on the character—which had initially inspired so much anxiety among comic fans—was, for me, the most satisfying Bat-manifestation yet. Positioned between the haunted Dark Knight of the comics, and the goofy charmer of the '60s series, this new Batman seemed less like an existentially enraged, near-biblically burdened martyr, and more like a too-smart-for-his-own-good weirdo. For an insane millionaire, he was relatable, so much so that many an impressionable mid-teen spent the fall of 1989 grabbing his or her friends, pulling them close, and grunting "I'm Batman." Being Batman looked like fun.
The immediate Batman sequels (and actors) that followed Batman Returns tried, in varying ways, to recapture the odd-duck feel that Keaton and Burton had embedded within the character. But sourpuss pin-up Val Kilmer couldn't fake the fun in 1995's Batman Forever, and even if he had, he would have been overshadowed by sentient ham-hocks Jim Carrey and Tommy Lee Jones. Meanwhile, George Clooney's Batman & Robin turn in 1997 was way too glib and hokey-jokey—no mean feat in a movie in which Uma Thurman dresses up as a sultry gorilla. By the end of the decade, Batman, and the Batman movies, had strayed from the gray but springy strangeness of the first two films, and gotten a little too light (and, for the sake of argument, I'm sticking with the flesh-and-blood Batman films here).
The Later, Darker Christopher Nolan Years
The necessary corrective would arrive a few years later, in 2005, with Christian Bale and Christopher Nolan's relentless, pained (but still occasionally funny) Batman, a tech-enabled bruiser facing down maniacs and devout terrorists. The Nolan films—more controlled than the previous entries, and intent on Grappling with Big Stuff—were action-packed and satisfyingly stark (for all my Keaton-stumping, 2008's *The Dark Knight *remains my favorite Batman movie). By the end of 2012's The Dark Knight Rises, though, the Cookie Puss growls and sad-pants scowls that had become the character's easily mockable hallmarks were starting to wear on me. On the big screen, Batman's glummy approach to everything was starting to feel one-dimensional.
I longed for a little more humor or jarring weirdness—for a Batman that seemed to enjoy being Batman, even just once in a while. I was the mook following Batman down the street on a hot summer's day: Come on, baby! You've got a nice smile! Use it or lose it!
But Batman never turned around. Instead, he kept on walking straight toward Batman v Superman: Dawn of Justice.
The Darkest Timeline: Zack Snyder's Batman
What can you say about a superhero movie in which two of the three main saviors seem neither particularly super nor heroic? About an action film in which we learn of the existence of four new, amazingly empowered characters via a series of grainy videos somebody watches on their hotel-room laptop? About a Serious Movie that features a scene in which Holly Hunter has a stare-down with mason jar full of urine?
All I can say is: Not my thing, thanks.
But maybe you loved Batman v Superman: Dawn of Justice. A lot of people did—even if few of them are employed as film critics—and, for the most part, I get why: There are swell explosions and some pummeling fights, and Snyder's camerawork has a sense of scale and space that other big action films lack. And Ben Affleck (whom I've always liked, even if I suspect he would have prank-called me in high school) is very good at playing privileged victims.
There's even a case to be made that one of the appeals of Dawn of Justice, and director Zack Snyder's Kill-'em-all Valhalla in general, is that they provide yet another needed corrective to the comic-movie canon. In his world, our superheroes are witnesses to (and often the cause of) massive losses of life and unquantifiable amounts of unearthly destruction. The Iron Man and Avengers films are also rife with such destruction—but even their most po-faced Marvel heroes can still occasionally make a joke. There's no such wisecrackery in Dawn of Justice; it has more sad-sack expressions than a Bright Eyes concert in 2002. It's as if Snyder wants us to realize that the price of having heroes in our lives means we either all end up dying, come close to dying, or just become perpetually bummed out by all the dying around us. Everybody's miserable with these guys around, and in that very weird, narrow way, Dawn of Justice is probably one of the more realistic superhero movies ever made.
There's no wisecrackery in Dawn of Justice; it has more sad-sack expressions than a Bright Eyes concert in 2002.
Affleck's Batman, meanwhile, feels equally true to life: He's embittered, depressed, overworked, and seemingly apathetic about sex (as much as I like Affleck and Gal Gadot's performances, the two have about as much heat as as pimento sandwich and a bicycle pump). He's become angry enough to brand his villains like cattle, and he doesn't even seem to get much satisfaction from detective work, which he mostly outsources to Alfred and some cool-seeming apps. He's pissed off and out for revenge, and he's probably the closest we've come to the hardened Batman that many comic book fans wanted to get on the big screen nearly 30 years ago.
Or, at least, that we thought we wanted. I'd be surprised if there weren't other former Batheads who walked out of Dawn of Justice thinking, "Wait—why did I like this character again?" Batman, for all his shadowy impulses, was once an aspirational figure. But it's hard to look at the gloomy version of him in *Batman v Superman—*the one whose every silent-sigh gesture looks as though it should be accompanied by bottom-of-the-screen depression-medication fine print—and think, "Man, that looks like a cool gig." By stripping him of any inner weirdness or levity or even the slightest inclination toward joy, Snyder has turned Batman into little more than a rich, angsty middle-aged white dude. Maybe that's who he really was all along. Either way, I don't need to see any more movies about those guys.
And Lord knows, if this is the kind of Batman that Snyder and Warner Bros. want to bring back to the big screen every few years (he'll cameo in this summer's Suicide Squad, and help anchor 2017's Justice League Part One, which I'm sure will begin with Darkseid flame-basting a Romanian orphanage), they certainly don't need to cater to me. In the last few decades, the character's become so malleable, and so prone to reinterpretation, that pretty much anyone can look at a particular era/title/movie and feel, "That's my Batman." There are plenty of people who will watch Dawn of Justice and think just that; I genuinely hope they enjoying digging into the character as much I did more than 30 years ago.
Yet I still hold out hope that, the next time Batman returns, Snyder and Affleck will grant the character a few moments of delight or absurdity or even just a hint of swaggering cuckoo-ness. He may be an insane trust-funder who dresses up as a winged mammal, but my Batman was also likably, heroically human. I miss him. And until he decides to come out of the shadows, I'll be in my cave with my back issues and Blu-rays, savoring every zap, boom, and pow.
#batman
#superheroes


Following an autopsy on the late officer of the Nigeria Security and Civil Defence Corps, NSCDC, Ochigbo Ogah allegedly killed by the Police, the result has revealed that his death was as a result of force and continuous torture.
This is contrary to claims by the Police that late Ochigbo Ogah Jumbo slumped and died while in their custody.
The late Jumbo, an Assistant Superintendent of NSCDC was March 20 reportedly killed by some police officers in the presence of his wife and kids in Nyanya, Abuja.
The Police, through the Force Public Relations Officer, ACP Frank Mba, swiftly dispelled the allegation, saying the late Jumbo slumped after driving himself to Nyanya Police station.
After unrelenting clamour by concerned members of the public and Jumbo's family, Mohammed Adamu, Inspector General of Police, ordered a comprehensive and speedy investigation into the circumstances of the death.
The result of an autopsy conducted at the Maitama General Hospital on 26th March 2019, revealed that late Jumbo died after suffering from "blunt force injury to the head and cerebral oedema" during the police brutality.
Sahara Reporters report that a copy of the autopsy report and the coroner's ordinances also confirmed that "there was no natural disease in the body to sufficiently explain this sudden death", as being peddled by the Police authority.
"Ada Jumbo, wife of the deceased, in an extract obtained from her statement, said her husband was dragged on the floor for several metres after he was mercilessly hit on the head with a batton.
"A family source also told our reporter that the Police authority had never visited nor shown sympathy to the family almost a month when "their breadwinner was gruesomely murdered", it said.


text:
cwd="$(cd "$(dirname "${BASH_SOURCE[0]}")" && pwd)"
source "$cwd/settings.sh"

#Packages are space seperated if there are multiple ones.
#You must change the below line to what you need.
packages="git svn"

#example list of packages:
#packages="lsof iftop git svn firewalld"

clear

#Create hidden file for each node - for status reporting.
for i in "${storageNodes[@]}"
do
    echo "-1" > $cwd/.$i
done

#Start the commands going in unison.
for i in "${storageNodes[@]}"
do

    printf $(ssh -o ConnectTimeout=$sshTimeout $i "yum install $packages -y > /dev/null 2>&1;echo \$?") > $cwd/.$i &

done

#Initially set completion status to false in order to enter into the loop.
complete="false"

#Run this loop until completion isn't false. This is the outter loop.
while [[ "$complete" == "false" ]]; do

    clear
    echo
    echo
    echo "Installing packages: $packages"
    echo
    complete="true"
    #Loop through each node to check status, this is the inner loop.
    for i in "${storageNodes[@]}"
    do

    status=$(cat $cwd/.$i)
    if [[ "$status" == "-1" ]]; then
        echo "$i...waiting for return"
        complete="false"
    elif [[ "$status" == "0" ]]; then
        echo "$i...Success!"
    else
        echo "$i...Failure!"
    fi

    done #Inner loop done.
    sleep 1 #Update frequency.
done #Outter loop done.

#Cleanup after all is done.
for i in "${storageNodes[@]}"
do
    rm -f $cwd/.$i
done

#Say it's done.
echo
echo "Complete"
echo

redpajama_set_name: RedPajamaGithub


text:
« Hiroshima Cover-up: How the War Department's Timesman Won a Pulitzer | 'Imperialist Powers Prepare Another Military Intervention in Libya' »
'Faceless body belonged to my sister': Hiroshima, Nagasaki Nuke Survivors Recall Horrors 70 Years On
5 August 2015 (RT)* – Blackened bodies, mothers who couldn't recognize their charred children and those still alive screaming with pain – these are horrific details the survivors of nuclear bombings of Hiroshima and Nagasaki recall ahead of 70th anniversary of the tragedy.
Nuclear weapons are the most destructive, inhumane and indiscriminate weapons ever created. Both in the scale of the devastation they cause, and in their uniquely persistent, spreading, genetically damaging radioactive fallout, they are unlike any other weapons. | Source: International Campaign to Abolish Nuclear Weapons (ICAN)
The US was the first nation to use nuclear weapons against an enemy target when they dropped atomic bombs on Japanese cities of Hiroshima and Nagasaki at the end of World War II on August 6 and 9, 1945.
More than 80,000 civilians died immediately as a result of the Hiroshima bomb – a device nicknamed 'Little Boy' by the US Air Force – and other 80,000 were believed killed in the Nagasaki attack by 'Fat Man'.
Thousands died from radiation sickness in the months and years following the blasts.
As of August 2014 the memorials in Hiroshima and Nagasaki list the names of more than 450,000 people who died in the tragedy: 292,325 in Hiroshima and 165,409 in Nagasaki.
Chiyoko Kuwabara, a survivor of Hiroshima atomic bombing, told RT that she was only 13 years old when the tragedy happened but the moments that changed her life forever still "linger in her memory."
"There were corpses all over the place and when a mother would walk looking for her kids she sometimes would hear cries calling 'mom…mom…' But even if they look at their children's faces they couldn`t recognize them. It was the children who recognize their mothers," Kuwabara said with tears in her eyes.
People like Kuwabara are called Hibakusha in Japan – a term for those who were exposed to radiation from the nuclear bombings.
READ MORE: Hiroshima, Nagasaki 70th anniversary: Anti-Trident activists join global fast against nukes
Kuwabara led RT team to Hiroshima Peace Memorial Museum which displays the horrors of the atomic bombing of the city: the damages caused by the bomb as well as photos of dying or dead people.
"It makes me suffer to look at these pictures…Poor people…I think they all died," she says, looking at the photos.
Kuwabara told RT that she feels disappointed by the current US administration of President Barack Obama.
"He [Obama] said he will reduce the nuclear weapons. Instead he is increasing it. Whatever beautiful words or acts he does I think America is not acting with sincerity. At least he should come to Hiroshima and Nagasaki and pay respects."
RT also spoke to a survivor of atomic bombing of Nagasaki, Sumiteru Taniguchi, who back in August 9, 1945 was delivering mail when a bomb fell on the city.
"I was 16 years old. Two kilometers from the epicenter I was walking and got the blast from behind. I could see it was from behind the light I was thrown," Taniguchi told RT.
The heat from the blast melted the skin on his back and left arm. The footage of his horrific injuries has become iconic and Taniguchi is now a living symbol of the suffering caused by the bombs.
The 86-year-old said that after the explosion he stayed in hospital three years and seven months and during his first year and nine months he was lying on his chest.
"My back was completely burned to the bones. And parts of my body hardened and the ribs got into my heart and lungs. It is very painful still today."
One more survivor of the Nagasaki bombings, Sanae Ikeda, 82, recalls how he lost his brothers and a sister in the tragedy.
"The explosion took away the skin of my hand and I started to bleed. The light was green and then I couldn't see anything."
In the middle of the road Ikeda saw someone – "a charred human being walking," he described to RT. He even couldn't figure out if it was a man or woman.
"Survivors who were badly hurt had no place to escape so everyone went to soak into a narrow stream of water running in the nearby."
Ikeda recalls horrible moment he saw the body of his sister which was completely deformed by the explosion.
"I found this body completely black, charred. I held it with my hands and it had no face Then I found that the string or ribbon of the waist of her pants. The outer part was all burned by the explosion, but inside the ribbon it was fine. I saw the little flowers and I could tell that this was the body of my little sister."
The bombings were approved by then US President Harry S Truman, who repeatedly stated that attacking Japan had saved lives on both sides.
"I think that the bombs were believed at the time to be necessary. as General [George] Marshall, who was head of the US military during the war said after the war, 'we didn't want to have to invade Japan,'" Richard Rhodes, an American historian, journalist and author who won a Pulitzer Prize for his book 'The Making of the Atomic Bomb', told RT.
"We knew we would kill many Japanese, and many Americans would die as well," he added.
But according to Peter Kuznick, professor of History and Director of the Nuclear Studies Institute at American University, the atomic bomb "wasn't necessary at all" to end the World War II.
"I think you can't come to any other conclusion than the bomb wasn't necessary, the Soviet invasion was going to end the war, and the US invasion was not going to begin till November first, so we dropped the bomb on August 6 and 9 to avoid an invasion that was not going to take place for three more months. Why do we do it? Well you have to conclude that we wanted to do it."
He added that if you look at the comments of US leaders at that time, "in fact, six or seven 5-star admirals and generals who got their fifth star during the war [WWII] are on record as saying that the bomb was either militarily unnecessary morally reprehensible or both."
*Source: RT. Go to Original.
Atomic Bombing – Hear the Story: Setsuko Thurlow
Atomic Bombing – Hear the Story: Yasuaki Yamashita
The Catastrophic Effects of Hiroshima and Nagasaki Atomic Bombings Still Being Felt Today
Why Nuclear Weapons?What Are the Most Significant Events of the Nuclear Age?Hiroshima Cover-up: How the War Department's Timesman Won a Pulitzer
Why Americans Believe That Bombing Hiroshima Was NecessaryMore on nuclear weapons:Don't Get Excited: Nuclear Disarmament Is Not on the Horizon Ban Nuclear Weapons – Now!
'Persisting Risk of Nuclear Weapons; Dangerous Return to Cold War Mentalities'
Nuclear Weapons Abolition – "NATO" Is Not an Excuse
Nuclear Weapons Abolition – 'US Attempts to Bully Allies into Inaction'
Tell Your Bank Not to Invest in Nuclear Weapons!
Initiative on Humanitarian Impact of Nuclear Weapons Takes Centre Stage at UN General Assembly
'The Damage Caused by Past Nuclear Testing Cannot Be Reversed'
Nuclear — Despite Price Dip, Uranium Demand, Production Continue to Rise
UN Officials Call for Renewed Global Commitment to Ending Nuclear Tests
Do You Have the Courage to Ban Nuclear Weapons?
Why Is the Total Elimination of Nuclear Weapons So Urgent?
Hiroshima: The Myth of "Military Necessity"
Inhumane, Illegal, Immoral and Cruel: a Survivor Account of the Hiroshima Bombing
'Humans Search for Life on Other Planets While Modernizing Weapons That Can Destroy All Life on Planet Earth'
Banks, Pension Funds, Insurance Companies in 30 Countries 'Invest' Your Money in Nuclear Arms
'Humanity Could Not Survive a Nuclear War Using Even a Fraction of Existing Arsenals'
Another Lost Chance to Save Middle East from Mass Destruction
Watch The Sky–It May Rain Atomic Bombs
Nuclear Terrorism – Killing 100,000 People Not Very Difficult
Humanitarian Consequences of Nuclear Weapons — Are You Ready to Hit the Gas?
Ecocide, a Catastrophic Consequence of Nuclear Weapons
"Breaking the Nuclear Chain" Campaign
Pressure to Push the Nuclear Genie Back in the Bottle
Germany Resolved to Pave the Way to Nuclear Disarmament
India, Pakistan Engaged in World's Most Active Nuclear Arms Race
World Nuclear Forces: 'Fewer But Newer' Weapons
Desert "Star Wars", Respect Dignity of Life
Nuclear Dangers, The World Is "One Minute Closer to Midnight" U.S. Spending on Atomic Bombs Doubles UN Budget
Of Dr. Strangelove and the Risk of Using Atomic Bombs World Campain Against False 'Nuclear Deterrence Doctrine'
The Story of Child Yami and the Atomic Bomb
Obama and How to Save a Quarter of a Trillion Dollars
You Choose: $105 Billion a Year for Health Care or Nuclear Weapons?
Read on nuclear Middle East:
Arabs Set to Create Their Own NATO, Urge a Nuclear-free Middle East
The Middle East Oil/Nuclear Puzzle
Anti-Nukes Move from Norway to Bahrain
The NPT's "Unacceptable and Continuous Failure": Egypt Walks Out
Fed Up With Empty Promises, The Arab May Abandon Nuclear Non-Proliferation Treaty
Middle East Nuclear Free Bid Moves to Finland – Yet Another Lost Chance?
Nuclear Free Middle East "High Priority" Nuclear Free Middle East — Necessary Yet Impossible
Middle East — France's Fuzzy Face on Nuclear Abolition
'Strong UN Commitment' to Nuclear-free Middle East Conference
Which Countries Have Nuclear Weapons and How Many?
Tactical Nuclear Weapons in Europe – The Dangers Are Very Great Today
Will Israel Attack Iran … Really?
Top US Military Commander: 'I Don't Want to Be Complicit' if Israel Attacks Iran
US Defense Secretary Warns of 'Pearl Harbor' Cyber Attack by Iran
Not a Time for Casual Games With Iran – Former Mossad Chief Warns
Posted on 05/08/2015 at 07:53 in Asia, Mother Earth, Others-USA-Europe-etc., The Peoples, War Lords	| RSS feed | Reply	| Trackback URL
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