text:
\section{Introduction}

As potential realizations of the Kitaev spin-1/2 model on the two-dimensional (2D) honeycomb lattice \cite{Kitaev2006,Nayak2008},
Kitaev materials (including A$_2$IrO$_3$ (A$=$Li, Na), $\alpha$-RuCl$_3$, etc.)  have attracted intensive research attentions in the past decade \cite{Jackeli2009,Chaloupka2010,Singh2010,Price2012,Singh2012,Plumb2014,Kim2015,Winter2016,Baek2017,Leahy2017,Sears2017,Wolter2017,Zheng2017,Rousochatzakis2017,Kasahara2018,Rau2014,Ran2017,Wang2017,Catuneanu2018,Gohlke2018,Liu2011,Chaloupka2013,Johnson2015,Motome2020}.
Motivated by the theoretical difficulties in strongly correlated systems in 2D, there has been a surge of research interests in studying 1D generalized Kitaev spin models \cite{Sela2014,Agrapidis2018,Agrapidis2019,Catuneanu2019,Yang2020,Yang2020a,Yang2020b,Yang2021b,Yang2022,Yang2022b,Yang2020c,Luo2021,Luo2021b,You2020,Sorensen2021}, which can be constructed by selecting one or several rows out of the honeycomb lattice.
The hope is that such 1D studies can help understand the 2D Kitaev physics, and indeed, it has been shown that the 2D zigzag order in the Kitaev-Heisenberg-Gamma model can be obtained by weakly coupling an infinite number of 1D chains \cite{Yang2022b}.

Besides providing hints for 2D physics, the 1D Kitaev spin models are also intriguing on their own, containing exotic strongly correlated physics.
For example, in the 1D spin-1/2 Kitaev-Gamma model, it has been found that about 67\% of the entire phase diagram is occupied by a gapless phase  whose low energy physics can be described by an emergent SU(2)$_1$ Wess-Zumino-Witten (WZW) model,
which is intimately related to the intricate discrete nonsymmorphic symmetry group of the system \cite{Yang2020}.
In addition to the emergent SU(2)$_1$ phase, the spin-1/2 Kitaev-Gamma chain also contains two magnetically ordered phases with symmetry breaking patterns $O_h\rightarrow D_4$ \cite{Yang2020} and $O_h\rightarrow D_3$ \cite{Yang2021b}, as well as another gapless phase with central charge $c=1/2$ located in the vicinity of the antiferromagnetic (AFM) Kitaev point \cite{Luo2021} , where $O_h$ is the full octahedral group and $D_n$ is the dihedral group of order $2n$, showcasing rich strongly correlated physics in such systems.

On the other hand, nearest neighbor Dzyaloshinskii-Moriya (DM) interactions \cite{Dzyaloshinskii1957,Dzyaloshinskii1964,Moriya1960,Fert1980,Fert1990} are ubiquitous in quantum magnetic systems which break the spatial inversion symmetry and can lead to exotic magnetic textures such as skyrmions \cite{Heinze2011,Yu2010,Bogdanov1994,Rolber2006} and chiral magnetic orders \cite{Dzyaloshinskii1965,Bogdanov1989}.
In Kitaev materials, the DM interactions can be conveniently induced and manipulated by external electric fields,
which have been studied under the context of  the electromagnetic controls of Kitaev materials \cite{Furuya2021,Chari2021}.
It is noteworthy to mention that the DM interactions in Kitaev materials exhibit a nonuniform bond-dependent structure.

In this work, we study the effects of a DM interaction in the 1D spin-1/2 Kitaev-Gamma model, which can be created by applying an electric field along the third direction (where the first and second directions refer to the two bond directions in the 1D model, see Fig. \ref{fig:bond_pattern} (a) for details).
Since in real Kitaev materials, the Kitaev and Gamma interactions usually dominate over other interactions such as the Heisenberg and $\Gamma^\prime$ terms,
our work  provides a perturbative starting point for the  analysis of more complicated interactions as well as an extrapolation  to 2D in the presence of a DM interaction.

We start from a pure Kitaev spin-1/2 chain with a DM interaction.
The first important result of our work is that there is a two-site periodic unitary transformation $V_2$, which maps the 1D Kitaev-DM model to the Kitaev-Gamma model and vice versa.
Using the known phase diagram of the 1D spin-1/2 Kitaev-Gamma model,
the effects of the DM interaction on the spin-1/2 Kitaev chain is thereby fully understood.

We then proceed to studying the 1D Kitaev-Gamma-DM model.
The strategy is to take the emergent SU(2)$_1$ phase in the Kitaev-Gamma chain as the unperturbed system, and treat the DM interaction as a perturbation.
Remarkably, although there is a dimension $3/2$ operator in the low energy conformal field theory (CFT), such operator is a total derivative and vanishes if periodic boundary condition is imposed.
Therefore, even with a nonzero DM interaction, the system remains to have an emergent SU(2)$_1$ conformal symmetry in an extended region in the phase diagram.
The theoretical predictions from perturbation theory are in excellent agreements with our  density matrix renormalization group (DMRG) numerical simulations.

Two observations are in order.
First, the aforementioned unitary transformation $V_2$ is a duality transformation which maps the Kitaev-Gamma-DM model to itself with a different set of parameters,
thereby enlarging the region occupied by the emergent SU(2)$_1$ phase in the phase diagram.
Second, it is interesting to compare the symmetry groups of the Kitaev-Gamma and Kitaev-Gamma-DM models.
The symmetry analysis is facilitated by a six-sublattice rotation $U_6$ \cite{Yang2020} which hold for both models.
In the $U_6$ frame, it has been shown in Ref. \onlinecite{Yang2020} that the symmetry group $G$ of the Kitaev-Gamma model satisfies $G/\mathopen{<}T_{3a}\mathclose{>}\cong O_h$ where $T_{na}$ represents the translation operator by $n$ sites.
On the other hand, the symmetry group $G_z$ of the Kitaev-Gamma-DM model is found to satisfy $G_z/\mathopen{<}T_{6a}\mathclose{>}\cong O_h$.
Hence, the symmetry group in the Kitaev-Gamma-DM model is ``halved" compared with the Kitaev-Gamma model.
Notice that the unit cell of the spin-1/2 Kitaev-Gamma-DM model contains an even number of sites, which naively corresponds to an integer spin.
Hence it is rather an unexpected result that such ``integer" spin system displays an emergent gapless phase at low energies,
which of course essentially originates from the intricate nonsymmorphic group structure.

The rest of the paper is organized as follows.
Sec. \ref{sec:model} introduces the model Hamiltonian and discusses the unitarily equivalent relations in the model.
In Sec. \ref{sec:KGDM_SU2_1}, the emergent SU(2)$_1$ conformal symmetry is obtained by treating the DM interaction as a perturbation on the known SU(2)$_1$ phase in the Kitaev-Gamma model.
Sec. \ref{sec:low_theory_DM_z} presents a symmetry analysis, which proves that the analysis in Sec. \ref{sec:KGDM_SU2_1} has exhausted all possible relevant and marginal operators in the low energy field theory.
Sec. \ref{sec:numerics} shows the numerical evidence for the emergent SU(2)$_1$ conformal symmetry.
Finally in Sec. \ref{sec:summary}, we summarize the main results of this work.

\section{The model}
\label{sec:model}

\subsection{Model Hamiltonian}

\begin{figure}[ht]
\begin{center}
\includegraphics[width=8cm]{bonds.pdf}
\caption{Bond patterns of the Kitaev-Gamma chain (a)  without sublattice rotation,
(b) after the six-sublattice rotation,
(c) with a nonzero DM interaction after six-sublattice rotation.
The black squares represent the unit cells.
} \label{fig:bond_pattern}
\end{center}
\end{figure}

The Hamiltonian of the spin-1/2 Kitaev-Gamma chain is defined as
\begin{eqnarray}
H=\sum_{\langle ij \rangle\in\gamma\,\text{bond}}\big[KS_i^\gamma S_j^\gamma+ \Gamma (S_i^\alpha S_j^\beta+S_i^\beta S_j^\alpha)\big],
\label{eq:Ham_KG}
\end{eqnarray}
in which $(\alpha,\beta,\gamma)$ form a right-handed coordinate system;
the pattern for the bond $\gamma$ is shown in Fig. \ref{fig:bond_pattern} (a);
and the couplings $K$ and $\Gamma$ can be parametrized as
$K=\cos(\psi)$,  $\Gamma=\sin(\psi)$.
Since the global spin rotation around $z$-axis by an angle $\pi$ (denoted as $R(\hat{z},\pi)$) changes the sign of $\Gamma$, it is enough to consider $\Gamma>0$, i.e., $\psi\in[0,\pi]$.
As shown by Ref. \onlinecite{Yang2020},
the system has an emergent SU(2)$_1$ conformal symmetry at low energies for $\theta\in[\psi_{c},\pi]$ where $\psi_{c} \sim 0.33\pi$.

In Kitaev materials, nearest neighbor DM interactions can be induced by applying electric fields.
Let $\gamma$ be the bond connecting nearest neighboring sites $i$ and $j$, and consider the right-handed coordinate system $(\gamma,\alpha,\beta)$.
An electric field is called in-plane if its direction is within the $\alpha\beta$-plane, and out-of-plane if it is parallel with the $\gamma$-axis.
As discussed in Ref. \onlinecite{Furuya2021},
an in-plane electric field induces a DM interaction of the form
\begin{eqnarray}} \def\eea{\end{eqnarray}
D_{M}(S_i^\alpha S_{i+1}^\beta-S_i^\beta S_{i+1}^\alpha).
\label{eq:D_Fz}
\eea

In this work, we consider the type of DM interaction which can be induced by an electric field along the $z$-direction.
As can be seen from  Fig. \ref{fig:bond_pattern} (a), an electric field along z-direction corresponds to an in-plane electric field for every bond in the chain.
Adding Eq. (\ref{eq:D_Fz}) to Eq. (\ref{eq:Ham_KG}),
the Hamiltonian becomes
\begin{eqnarray}
H_z=\sum_{\langle ij \rangle\in\gamma\,\text{bond}}\big[KS_i^\gamma S_j^\gamma+ \Gamma_1 S_i^\alpha S_j^\beta+\Gamma_2 S_i^\beta S_j^\alpha\big],
\label{eq:Ham_KG_z}
\end{eqnarray}
in which
\begin{eqnarray}} \def\eea{\end{eqnarray}
\Gamma_1=\Gamma+D_M,~\Gamma_2=\Gamma-D_M;
\eea
the bond pattern for $\gamma$ is shown in Fig. \ref{fig:bond_pattern} (a);
and  $(\gamma\alpha\beta)$ form a right-handed coordinate system.
 More explicitly, the form of the Hamiltonian within a two-site unit cell of sites $\{1,2\}$ is given by
\begin{eqnarray}} \def\eea{\end{eqnarray}
H_{z,12} &=&  K S^x_1 S^x_2 + \Gamma_1 S^y_1 S^z_2+\Gamma_2 S^z_1 S^y_2,\nonumber \\
H_{z,23} &=& K S^y_2 S^y_3 + \Gamma_1 S^z_2 S^x_3+\Gamma_2 S^x_2 S^z_3.
\label{eq:H}
\eea

Finally, a useful parametrization is
\begin{eqnarray}} \def\eea{\end{eqnarray}
K&=&\cos(\theta),\nonumber\\
D_M&=&\sin(\theta)\cos(\phi),\nonumber\\
\Gamma&=&\sin(\theta)\sin(\phi),
\label{eq:parametrize_KGDM}
\eea
in which $\theta\in(0,\pi)$, $\phi\in(0,2\pi)$.
Hence, the full parameter  space of the model is a unit sphere.

\subsection{Six-sublattice rotation}

A useful unitary transformation is the  six-sublattice rotation $U_6$, defined as
\begin{eqnarray}
\text{Sublattice $1$}: & (x,y,z) & \rightarrow (x^{\prime},y^{\prime},z^{\prime}),\nonumber\\
\text{Sublattice $2$}: & (x,y,z) & \rightarrow (-x^{\prime},-z^{\prime},-y^{\prime}),\nonumber\\
\text{Sublattice $3$}: & (x,y,z) & \rightarrow (y^{\prime},z^{\prime},x^{\prime}),\nonumber\\
\text{Sublattice $4$}: & (x,y,z) & \rightarrow (-y^{\prime},-x^{\prime},-z^{\prime}),\nonumber\\
\text{Sublattice $5$}: & (x,y,z) & \rightarrow (z^{\prime},x^{\prime},y^{\prime}),\nonumber\\
\text{Sublattice $6$}: & (x,y,z) & \rightarrow (-z^{\prime},-y^{\prime},-x^{\prime}),
\label{eq:6rotation}
\end{eqnarray}
in which ``Sublattice $i$" ($1\leq i \leq 6$) represents all the sites $i+6n$ ($n\in \mathbb{Z}$) in the chain, and we have abbreviated $S^\alpha$ ($S^{\prime \alpha}$) as $\alpha$ ($\alpha^\prime$) for short ($\alpha=x,y,z$).

In the six-sublattice rotated frame, the Hamiltonian is
\begin{eqnarray}} \def\eea{\end{eqnarray}
H^\prime_z=\sum_{\langle ij \rangle\in\gamma\,\text{bond}}\big[-KS_i^\gamma S_j^\gamma - \Gamma_1 S_i^\alpha S_j^\alpha- \Gamma_2 S_i^\beta S_j^\beta\big],
\label{eq:Ham_rot}
\eea
in which
$\gamma\in\{x,\bar{z},y,\bar{x},z,\bar{y}\}$ has a six-site periodicity as shown in Fig. \ref{fig:bond_pattern} (c);
$S_j^\gamma=S_j^{\bar{\gamma}}$;
 $(\gamma\alpha\beta)$ form a right-handed coordinate system for $\gamma\in\{x,y,z\}$, and they form a left-handed system when $\gamma\in\{\bar{x},\bar{y},\bar{z}\}$.
 More explicitly, the form of the Hamiltonian within a six-site unit cell of sites $\{1,2,3,4,5,6\}$ is
 \begin{eqnarray}} \def\eea{\end{eqnarray}
H^{\prime}_{z,12} &=&  -K S^{ x}_1 S^{ x}_2-\Gamma_1 S^{ y}_1 S^{ y}_2-\Gamma_2 S^{ z}_1 S^{ z}_2, \nonumber \\
H^{\prime}_{z,23} &=& -K S^{z }_2 S^{ z}_3-\Gamma_1 S^{ y}_2 S^{ y}_3-\Gamma_2 S^{ x}_2 S^{ x}_3, \nonumber \\
H^{\prime}_{z,34} &=& -K S^{ y}_3 S^{ y}_4-\Gamma_1 S^{ z}_3 S^{ z}_4-\Gamma_2 S^{ x}_3 S^{ x}_4, \nonumber \\
H^{\prime}_{z,45} &=& -K S^{ x}_4 S^{ x}_5-\Gamma_1 S^{ z}_4 S^{ z}_5-\Gamma_2 S^{ y}_4 S^{ y}_5, \nonumber \\
H^{\prime}_{z,56} &=& -K S^{z }_5 S^{ z}_6-\Gamma_1 S^{ x}_5 S^{ x}_6-\Gamma_2 S^{ y}_5 S^{ y}_6, \nonumber \\
H^{\prime}_{z,67} &=& -K S^{ y}_6 S^{ y}_7-\Gamma_1 S^{ x}_6 S^{ x}_7-\Gamma_2 S^{ z}_6 S^{ z}_7.
\label{eq:Hprime}
\eea

 Form here on, we stick to the six-sublattice rotated frame in this work unless otherwise stated.

\subsection{Unitarily equivalent relations}

Clearly, both $\Gamma_1$ and $\Gamma_2$ change sign under $R(\hat{z},\pi)$ within the original frame (i.e., without six-sublattice rotation $U_6$).
Hence there is the equivalence
\begin{eqnarray}} \def\eea{\end{eqnarray}
(K,\Gamma,D_M)\simeq (K,-\Gamma,-D_M).
\label{eq:equiv1}
\eea
Because of Eq. (\ref{eq:equiv1}), it is enough to consider the  $\Gamma>0$ region.

In addition, consider a two-sublattice rotation $V_2$ which acts on odd sites as a spin rotation $R(\hat{z},\pi)$ but leaves all even sites unchanged.
Straightforward calculations show that the Kitaev, Gamma and DM terms transform under $V_2$ as
\begin{eqnarray}} \def\eea{\end{eqnarray}
KS_i^\gamma S_j^\gamma &\rightarrow& -KS_i^\gamma S_j^\gamma,\nonumber\\
\Gamma (S_i^\alpha S_j^\beta+S_i^\beta S_j^\alpha) &\rightarrow& -\Gamma (S_i^\alpha S_j^\beta-S_i^\beta S_j^\alpha),\nonumber\\
D_{M}(S_i^\alpha S_{i+1}^\beta-S_i^\beta S_{i+1}^\alpha) &\rightarrow& -D_M (S_i^\alpha S_{i+1}^\beta+S_i^\beta S_{i+1}^\alpha),\nonumber\\
\label{eq:equiv_V6_KGammaDM}
\eea
which hold for every bond.
Hence, we also have the following equivalence
\begin{eqnarray}} \def\eea{\end{eqnarray}
(K,\Gamma,D_M)\simeq (-K,-D_M,-\Gamma).
\label{eq:equivalence}
\eea

In terms of $(\theta,\phi)$ in Eq. (\ref{eq:parametrize_KGDM}), the equivalences in Eqs. (\ref{eq:equiv1},\ref{eq:equivalence}) can be expressed as $(\theta,\phi)\simeq (\theta,-\phi)\simeq (\pi-\theta,\frac{3\pi}{2}-\phi)$.
Therefore, it is enough to consider the region $\theta\in(0,\frac{\pi}{2})$, $\phi\in(0,\pi)$ in the phase diagram where $\theta$ and $\phi$ are defined in Eq. (\ref{eq:parametrize_KGDM}).

\begin{figure}[ht]
\begin{center}
\includegraphics[width=6cm]{phase_KDM.pdf}
\caption{Phase diagram of the spin-1/2 Kitaev chain with DM interaction, where $K=\cos(\phi^\prime)$, $D_M=\sin(\phi^\prime)$.
} \label{fig:phase_KDM}
\end{center}
\end{figure}

Using Eq. (\ref{eq:equivalence}), it can be seen that the Kitaev-DM model is mapped to the  Kitaev-Gamma model.
On the other hand, the phase diagram of the spin-1/2 Kitaev-Gamma chain has been studied in detail in Ref. \onlinecite{Yang2020} and Ref. \onlinecite{Yang2021b}.
Therefore, we are able to directly obtain the phase diagram of the spin-1/2 Kitaev chain with a DM interaction as shown in Fig. \ref{fig:phase_KDM},
in which $K$ and $D_M$ are parametrized as
\begin{eqnarray}} \def\eea{\end{eqnarray}
K=\cos(\phi^\prime),~D_M=\sin(\phi^\prime),
\eea
and the values of the phase transition points are
$\phi^\prime_c=0.67\pi$, $\phi^\prime_{c1}=0.9\pi$, $\phi^\prime_{c2}=0.967\pi$,
and $\bar{\phi^\prime}_c=2\pi-\phi^\prime_c$, $\bar{\phi}^\prime_{c1}=2\pi-\phi^\prime_{c1}$, $\bar{\phi}^\prime_{c2}=2\pi-\phi^\prime_{c2}$.
Since $D_M$  changes sign under $R(\hat{z},\pi)$ whereas $K$ remains the same,
it is enough to consider the region $\phi^\prime\in[0,\pi)$.
For $\phi^\prime\in(0,\phi_c)$, the system is in a gapless phase which has an emergent SU(2)$_1$ conformal symmetry at low energies;
for $\phi^\prime\in(\phi^\prime_c,\phi^\prime_{c1})$, the system is in an ordered phase with a spontaneous symmetry breaking pattern as $O_h\rightarrow D_4$;
for $\phi^\prime\in(\phi^\prime_{c1},\phi^\prime_{c2})$, the system is in another ordered phase with a spontaneous symmetry breaking pattern as $O_h\rightarrow D_3$;
for $\phi^\prime\in(\phi^\prime_{c2},\pi)$ named as ``Kitaev" in Fig. \ref{fig:phase_KDM}, there is numerical evidence that the central charge in this region is $c=1/2$ \cite{Luo2021}.

\section{Emergent SU(2)$_1$ conformal symmetry in the spin-1/2 Kitaev-Gamma-DM chain}
\label{sec:KGDM_SU2_1}

In this section, we study the spin-1/2 Kitaev-Gamma chain with a bond-dependent DM interaction, which can be induced by an electric field along $z$-direction.

Fig. \ref{fig:phase_KGDM} is a schematic plot of the front half of the unit sphere of the parameter space in terms of $\theta$ and $\phi$ as defined in Eq. (\ref{eq:parametrize_KGDM}).
The back half of the sphere is not shown because of the equivalence in Eq. (\ref{eq:equiv1}).
We will analytically demonstrate that there is an emergent SU(2)$_1$ conformal symmetry at low energies in the ``Emergent SU(2)$_1$ I" region in Fig. \ref{fig:phase_KGDM}, which is analyzed by perturbing the Kitaev-Gamma model and treating the DM interaction as a perturbation.
Then by using Eq. (\ref{eq:equiv1}) and Eq. (\ref{eq:equivalence}),
we know that the regions marked with ``Emergent SU(2)$_1$ II, III" also have an emergent SU(2)$_1$ conformal symmetry at low energies.

We emphasize that the phase diagram in Fig. \ref{fig:phase_KGDM} is only schematic.
The phase boundaries of the three emergent SU(2)$_1$ regions are shown as dashed lines since their locations  are not precisely determined.
On the other hand, the phase transitions in the Kitaev-DM and Kitaev-Gamma models are known, which are shown as the red, brown and green cross symbols in Fig. \ref{fig:phase_KGDM}, corresponding to $\phi^\prime_c$, $\phi^\prime_{c1}$ and $\phi^\prime_{c2}$ (or $\bar{\phi}^\prime_c$, $\bar{\phi}^\prime_{c1}$ and $\bar{\phi}^\prime_{c2}$) in Fig. \ref{fig:phase_KDM}, respectively.

\begin{figure}[ht]
\begin{center}
\includegraphics[width=7cm]{phase_KGDM.pdf}
\caption{Schematic plot of the emergent SU(2)$_1$ phases in the phase diagram of the spin-1/2 Kitaev-Gamma chain with a DM interaction.
The red, brown and green cross symbols correspond to the phase transitions at $\phi^\prime_c$, $\phi^\prime_{c1}$ and $\phi^\prime_{c2}$ (or $\bar{\phi}^\prime_c$, $\bar{\phi}^\prime_{c1}$ and $\bar{\phi}^\prime_{c2}$) in Fig. \ref{fig:phase_KDM}, respectively,
in either the Kitaev-Gamma model or Kitaev-DM model.
}
\label{fig:phase_KGDM}
\end{center}
\end{figure}

\subsection{Low energy field theory}
\label{subsec:Low_field_theory}

In this subsection, treating the DM term as a perturbation, we derive the low energy field theory of the model.
We will consider the $K<0$, $\Gamma<0$ region, which is in the back half of the sphere (not shown in Fig. \ref{fig:phase_KGDM}).
This region is equivalent with ``Emergent SU(2)$_1$ I" phase in Fig. \ref{fig:phase_KGDM} according to Eq. (\ref{eq:equiv1}).

\subsubsection{Review of SU(2)$_1$ CFT for spin-1/2 Kitaev-Gamma chain}

When $K=\Gamma_1=\Gamma_2<0$, the system in Eq. (\ref{eq:Ham_rot}) reduces to the AFM Heisenberg model, which represents a hidden SU(2) symmetric point.
It is known that at low energies,  the spin-1/2 AFM Heisenberg model is described by the SU(2)$_1$ Wess-Zumino-Witten (WZW) model.
The Hamiltonian density is of the Sugawara form
\begin{eqnarray}} \def\eea{\end{eqnarray}
\mathcal{H}=\frac{2\pi}{3}v (\vec{J_L}\cdot \vec{J_L}+\vec{J_R}\cdot \vec{J_R})
\eea
with an additional marginally irrelevant term $-u\vec{J_L}\cdot \vec{J_R}$,
in which $v$ is the spin velocity; $u>0$ is the coupling constant of the marginally irelevant term $\vec{J_L}\cdot \vec{J_R}$;
and $\vec{J_L}$ and $\vec{J_R}$ defined by
\begin{eqnarray}} \def\eea{\end{eqnarray}
\vec{J_L}&=&-\frac{1}{4\pi}\text{tr} [(\partial_z g) g^\dagger \vec{\sigma}] \nonumber\\
\vec{J_R}&=&\frac{1}{4\pi}\text{tr} [g^\dagger (\partial_{\bar{z}} g) \vec{\sigma}],
\label{eq:J_LR}
\eea
are the left and right WZW currents, respectively,
where the SU(2) matrix $g$ is the WZW primary field, $\sigma^{\alpha}$ ($\alpha=x,y,z$) are the three Pauli matrices,
and $z=\tau+ix$ ($\bar{z}=\tau-ix$) is the holomorphic (anti-holomorphic) coordinate in the imaginary time formalism.
This hidden SU(2) symmetric AFM point provides a starting point for a field theory perturbation for the regions nearby.

When $D_M=0$ but $K\neq \Gamma$, the system in Eq. (\ref{eq:Ham_rot}) reduces to the Kitaev-Gamma model,
and it has been shown in Ref. \onlinecite{Yang2020} that the system is described by the SU(2)$_1$ WZW model at low energies.
The spin operators are related to the SU(2)$_1$ low energy fields by the nonsymmorphic nonabelian bosonization formula:
\begin{eqnarray}} \def\eea{\end{eqnarray}
\frac{1}{a}S_{i+3n}^\alpha=D^\alpha_{i} (J_L^\alpha+ J_R^\alpha)+C^\alpha_{i} \frac{1}{\sqrt{a}} (-)^{n} N^\alpha,
\label{eq:nonsymmorphic_bosonize}
\eea
in which $i=1,2,3$; $\alpha=x,y,z$;
and
\begin{flalign}
&D_1^z=D_2^y=D_3^x (=D_1),\nonumber\\
&D_1^x=D_2^z=D_3^y=D_1^y=D_2^x=D_3^z (=D_2),\nonumber\\
&C_1^z=C_2^y=C_3^x (=C_1),\nonumber\\
&C_1^x=C_2^z=C_3^y=C_1^y=C_2^x=C_3^z (=C_2).
\end{flalign}

\subsubsection{Low energy Hamiltonian for nonzero DM interaction}

When $D_M\neq 0$, in the six-sublattice rotated frame,
the perturbation is
\begin{eqnarray}} \def\eea{\end{eqnarray}
\Delta H^\prime=D_M\sum_{<ij>\in\gamma\,\text{bond}}(-S_i^\alpha S_j^\alpha+ S_i^\beta S_j^\beta),
\label{eq:DeltaH_D}
\eea
in which $\gamma\in\{x,\bar{z},y,\bar{x},z,\bar{y}\}$;
 $(\alpha\beta\gamma)$ form a right-handed coordinate system for $\gamma\in\{x,y,z\}$, and  form a left-handed system when $\gamma\in\{\bar{x},\bar{y},\bar{z}\}$.

By treating $D_M$ as a perturbation on the Kitaev-Gamma model,  we use Eq. (\ref{eq:nonsymmorphic_bosonize}) to express Eq. (\ref{eq:DeltaH_D}) in terms of the SU(2)$_1$ low energy degrees of freedom.
To proceed on, we need  several operator product expansions (OPE) in the SU(2)$_1$ theory.
Using the following OPE \cite{DiFrancesco1997},
\begin{flalign}
&\vec{J}_L(w) g(z,\bar{z})= -\frac{1}{2} \frac{\vec{\sigma} g(z,\bar{z}) }{w-z} +:\vec{J}_Lg: (z,\bar{z})+O(|z-w|),\nonumber\\
&\vec{J}_R(w) g(z,\bar{z})= \frac{1}{2} \frac{ g(z,\bar{z})  \vec{\sigma}}{w-z} +:\vec{J}_Rg: (z,\bar{z})+O(|z-w|),
\label{eq:OPE_Jg}
\end{flalign}
we obtain ($\alpha=x,y,z$),
\begin{eqnarray}
iJ_L^\alpha(x) \text{tr} (g(x+d)\sigma^\alpha
&=&\frac{1}{4\pi  d}\epsilon+:J_L^\alpha N^\alpha:,\nonumber\\
iJ_R^\alpha(x) \text{tr} (g(x+d)\sigma^\alpha
&=&\frac{1}{4\pi  d}\epsilon+:J_R^\alpha N^\alpha:,\nonumber\\
i\text{tr} (g(x)\sigma^\alpha)J_L^\alpha(x+d
&=&-\frac{1}{4\pi  d}\epsilon+:J_L^\alpha N^\alpha:,\nonumber\\
i\text{tr} (g(x)\sigma^\alpha)J_R^\alpha(x+d
&=&-\frac{1}{4\pi  d}\epsilon+:J_R^\alpha N^\alpha:,
\label{eq:OPE_2}
\end{eqnarray}
in which
\begin{eqnarray}} \def\eea{\end{eqnarray}
\epsilon&=&\text{tr}(g), \nonumber\\
N^\alpha&=&i \text{tr}(g\sigma^\alpha),
\label{eq:epsilon_N}
\eea
and the symbol $:AB:$ means the $O(d^0)$ term in the full OPE $A(x+d)B(x)$.

Plugging Eq. (\ref{eq:nonsymmorphic_bosonize}) and Eq. (\ref{eq:OPE_2}) into $S_i^\alpha S_{i+1}^\alpha$, we obtain
\begin{eqnarray}} \def\eea{\end{eqnarray}
&&S_i^\alpha S_{i+1}^\alpha\nonumber\\
&=& a^2 D_i^\alpha D_{i+1}^\alpha [J_L^\alpha(x)+J_R^\alpha(x)][J_L^\alpha(x+a)+J_R^\alpha(x+a)]\nonumber\\
&&-aC_i^\alpha C_{i+1}^\alpha N^\alpha(x) N^\alpha(x+a) \nonumber\\
&&+(-)^i a^{3/2} \big[
-\frac{1}{2\pi a}(D_i^\alpha C_{i+1}^\alpha+C_i^\alpha D_{i+1}^\alpha)\epsilon \nonumber\\
&&+(C_i^\alpha D_{i+1}^\alpha-D_i^\alpha C_{i+1}^\alpha) :(J_L^\alpha+J_R^\alpha)N^\alpha:
\big].
\label{eq:bosonize_SS}
\eea
We note that in Eq. (\ref{eq:bosonize_SS}), the second and third lines are full OPE,
however, their exact expressions are not important for us.
Then plugging Eq. (\ref{eq:bosonize_SS}) into Eq. (\ref{eq:DeltaH_D}) and summing over the  three sites within a unit cell, we arrive at
\begin{flalign}
\Delta H^\prime = -D_M(C_1D_2-C_2D_1)\int dx :(\vec{J}_L+\vec{J}_R)\cdot\vec{N}:.
\label{eq:Delta_H_JN}
\end{flalign}
Clearly, the $:(\vec{J}_L+\vec{J}_R)\cdot\vec{N}:$ term does not vanish when $C_1D_2-C_2D_1\neq 0$,
which is the case except $K=\Gamma$.
In fact, when $K=\Gamma$, the $:(\vec{J}_L+\vec{J}_R)\cdot\vec{N}:$ term only appears at the second nearest neighbor level which is discussed in detail in Appendix \ref{app:2nd_quadrupole}.
Here we note that we have essentially performed a first order perturbative treatment by directly projecting the Hamiltonian into the low energy space.

To summarize, the low energy Hamiltonian is given by
\begin{eqnarray}} \def\eea{\end{eqnarray}
\mathcal{H}&=&\frac{2\pi v}{3} \int dx :(\vec{J}_L\cdot \vec{J}_L+\vec{J}_R\cdot \vec{J}_R):-u\int dx \vec{J}_L\cdot \vec{J}_R\nonumber\\
&&-D_M(C_1D_2-C_2D_1) \int dx :(\vec{J}_L+\vec{J}_R)\cdot \vec{N}:.
\label{eq:low_energy_theory2}
\eea

\subsection{Emergent SU(2)$_1$ conformal symmetry}
\label{sec:emergent_SU2}

At first sight, the system opens a gap at low energies since the scaling dimension of  $:(J^\alpha_L+J^\alpha_R) N^\alpha:$ is $3/2$ which is a relevant operator.
However,  $:(J^\alpha_L+J^\alpha_R) N^\alpha:$ is a total derivative in the SU(2)$_1$ WZW model,  hence it has no effect in the low energy Hamiltonian.
There is a quick way to see this.
In abelian bosonization, we have (up to  overall constant factors) \cite{Giamarchi2004}
\begin{eqnarray}} \def\eea{\end{eqnarray}
J^z&=&-\frac{1}{\pi}\nabla \varphi,\nonumber\\
N^z&=& \frac{1}{\pi } \cos(2\varphi),
\eea
in which $\varphi$ is the field in the Luttinger liquid Hamiltonian
\begin{eqnarray}} \def\eea{\end{eqnarray}
H_{LL}=\frac{v}{2\pi} \int dx [\kappa^{-1} (\nabla \varphi)^2 +\kappa (\nabla \theta)^2].
\eea
It is clear that $J^zN^z=-\frac{1}{2\pi^2}\nabla \sin(2\varphi)$ is a total derivative.
Since the SU(2)$_1$ WZW model has SU(2) symmetry, $:J^xN^x:$ and $:J^yN^y:$ must also be total derivatives.
In fact, based on the OPE relations in the SU(2)$_1$ WZW model, a rigorous proof of $:(J^\alpha_L+J^\alpha_R) N^\alpha:$ being a total derivative can be given as  discussed in Appendix \ref{app:total_derivative}, which shows that
\begin{eqnarray}} \def\eea{\end{eqnarray}
:(\vec{J}_L+\vec{J}_R) \cdot \vec{N}:=-3\nabla \epsilon.
\eea

Dropping the $:(J^\alpha_L+J^\alpha_R) N^\alpha:$ term, Eq. (\ref{eq:low_energy_theory2}) becomes
\begin{flalign}
\mathcal{H}&=&\frac{2\pi v}{3} \int dx :(\vec{J}_L\cdot \vec{J}_L+\vec{J}_R\cdot \vec{J}_R):-u\int dx \vec{J}_L\cdot \vec{J}_R,
\label{eq:low_energy_theory_2}
\end{flalign}
which remains to have an emergent SU(2)$_1$ conformal symmetry even for nonzero $D_M$,
as along as $D_M$ is small enough such that a perturbative analysis is valid.

\section{Symmetry analysis }
\label{sec:low_theory_DM_z}

The analysis in Sec. \ref{subsec:Low_field_theory} is only based on a first order perturbative treatment.
To fully confirm that except $:(J^\alpha_L+J^\alpha_R) N^\alpha:$, there is no other additional relevant or marginal term (i.e., having scaling dimension less than or equal to two) in the low energy field theory compared with the $D_M=0$ case, we perform a symmetry analysis to analyze all the symmetry allowed terms among the relevant and marginal operators.
This is a proof for the emergent SU(2)$_1$ conformal symmetry for small enough $D_M$.
In addition, in Sec. \ref{sec:nonsymmor_bosonize}, we derive the nonsymmorphic nonabelian bosonization formulas which only respect the exact discrete nonsymmorphic symmetry group, not the emergent SU(2) symmetry.

For simplification of notation, we will write $:AB:$ as $AB$ in what follows, which is understood as a normal ordered product.

\subsection{Nonsymmorphic symmetry group}

We first analyze the symmetry group of the model in the six-sublattice rotated frame.
The Hamiltonian $H^\prime_z$ in Eq. (\ref{eq:Ham_rot}) is invariant under the following symmetry operations,
\begin{eqnarray}
1.&T &:  (S_i^x,S_i^y,S_i^z)\rightarrow (-S_{i}^x,-S_{i}^y,-S_{i}^z)\nonumber\\
2.& R_a^{-1}T_{2a}&:  (S_i^x,S_i^y,S_i^z)\rightarrow (S_{i+2}^y,S_{i+2}^z,S_{i+2}^x)\nonumber\\
3.&R_I I&: (S_i^x,S_i^y,S_i^z)\rightarrow (-S_{4-i}^z,-S_{4-i}^y,-S_{4-i}^x)\nonumber\\
4.&R(\hat{x},\pi) &:  (S_i^x,S_i^y,S_i^z)\rightarrow (S_i^x,-S_i^y,-S_i^z)\nonumber\\
5.&R(\hat{y},\pi) &:  (S_i^x,S_i^y,S_i^z)\rightarrow (-S_i^x,S_i^y,-S_i^z)\nonumber\\
6.&R(\hat{z},\pi) &:  (S_i^x,S_i^y,S_i^z)\rightarrow (-S_i^x,-S_i^y,S_i^z),
\label{eq:symmetries_Ez}
\end{eqnarray}
in which $R(\hat{n},\phi)$ denotes a rotation around $\hat{n}$-direction by an angle $\phi$;
$T_{na}$ represents the translation operator by $n$ sites;
$R_a$ is the rotation around $(1,1,1)$-direction by $2\pi/3$;
and $R_I$ is a $\pi$-rotation around the $(1,0,-1)$-direction.
The symmetry group $G$ is generated by the operations in Eq. (\ref{eq:symmetries_Ez}), i.e.,
\begin{eqnarray}} \def\eea{\end{eqnarray}
G_z=\mathopen{<}T, R_a^{-1}T_{2a},R_I I,R(\hat{x},\pi),R(\hat{y},\pi),R(\hat{z},\pi)\mathclose{>}.
\label{eq:Gz}
\eea

We note that $G_z$ is very similar to the symmetry group $G_d$ of the dimerized Kitaev-Gamma chain discussed in Ref. \onlinecite{Yang2022}.
The symmetry operations of $G_z$ and $G_d$ overlap except the inversion symmetry: The inversion center for the inversion operation in $G_z$ is a site, whereas it is located at the middle point of the bond for $G_d$.
However,  this difference has notable physical effects:
The dimerized spin-1/2 Kitaev-Gamma model is in a disordered phase with a nonzero spin gap,  whereas the spin-1/2 Kitaev-Gamma-DM model is gapless having an emergent SU(2)$_1$ conformal symmetry at low energies.
It is worth to mention that the group structure of $G_z$ satisfies $G_z/\mathopen{<}T_{6a}\mathclose{>}\simeq O_h$ where $O_h$ is the full octahedral group, which can be proved in a same way as what is done for $G_z$ in Ref. \onlinecite{Yang2022}.

\subsection{Symmetry analysis of the low energy Hamiltonian}

Sec. \ref{subsec:Low_field_theory} demonstrates the existence of the $(J^\alpha_L+J^\alpha_R) N^\alpha$ term.
In this section, by exploiting a symmetry analysis, we prove that there is no other relevant operators in the low energy field theory.

The symmetry transformation properties of the WZW fields under spin rotations, time reversal, and inversion operations are summarized in Appendix \ref{app:transform_WZW}.
An analysis of all relevant and marginal operators in the SU(2)$_1$ WZW model based on symmetry considerations is as follows.

1) $\epsilon$ is forbidden by $R_II$.

2) $N^\alpha$ ($\alpha=x,y,z$) are forbidden by $T$.

3) $J^\alpha$ ($\alpha=x,y,z$) are forbidden by $R(\hat{\beta},\pi)$ where $\beta\neq \alpha$.

4) $J^\alpha_L\epsilon,J^\alpha_R\epsilon$ are forbidden by $R(\hat{\beta},\pi)$ where $\beta\neq \alpha$.

5) Within $J^\alpha_LN^\beta,J^\alpha_RN^\beta$, the only symmetry allowed interaction is
$(\vec{J}_L+\vec{J}_R)\cdot \vec{N}$.

6) For $J_L^\alpha J_R^\beta$, the only symmetry allowed term is
$\vec{J}_L \cdot\vec{J}_R$.

According to the above analysis, the symmetry allowed low energy Hamiltonian is given by
\begin{eqnarray}} \def\eea{\end{eqnarray}
\mathcal{H}&=&\frac{2\pi v}{3} \int dx (\vec{J}_L\cdot \vec{J}_L+\vec{J}_R\cdot \vec{J}_R)-u\int dx \vec{J}_L\cdot \vec{J}_R\nonumber\\
&&+\lambda \int dx (\vec{J}_L+\vec{J}_R)\cdot \vec{N}.
\label{eq:low_energy_theory}
\eea
Indeed, $(J^\alpha_L+J^\alpha_R) N^\alpha$ is the only symmetry allowed relevant operator in the low energy Hamiltonian.
The emergent SU(2)$_1$ conformal symmetry then follows from the observation that the $(J^\alpha_L+J^\alpha_R) N^\alpha$ term is a total derivative
as discussed in Sec. \ref{sec:emergent_SU2}.
It is noteworthy to mention that the Hamiltonian in Eq. (\ref{eq:low_energy_theory}) is SU(2) invariant although the symmetry group is discrete and nonsymmorphic.

\subsection{Nonsymmorphic nonabelian bosonization formulas}
\label{sec:nonsymmor_bosonize}

In this subsection, we derive the nonsymmorphic nonabelian bosonization formulas for the Kitaev-Gamma-DM model based on a symmetry analysis.
These formulas only respect the exact nonsymmorphic symmetry group $G_z$ in Eq. (\ref{eq:Gz}), but break the emergent SU(2) symmetry.

In general, the local spin operators are related to the SU(2)$_1$ low energy degrees of freedom via the following relations,
\begin{eqnarray}} \def\eea{\end{eqnarray}
S_j^\alpha&=& \sum_\beta[ D_{L,j}^{\alpha\beta} J^\beta_L+D_{R,j}^{\alpha\beta} J^\beta_R +(-)^j C_j^{\alpha\beta} N^\beta],
\label{eq:bosonizaion_1}
\eea
in which $\alpha,\beta=x,y,z$.
First, since time reversal symmetry switches the left and right movers, we have
\begin{eqnarray}} \def\eea{\end{eqnarray}
D_{L,j}^{\alpha\beta}=D_{R,j}^{\alpha\beta}=D_{j}^{\alpha\beta}.
\eea
Second, since $R(\hat{\alpha},\pi)$ ($\alpha=x,y,z$) leaves the system invariant, it is clear that the cross coefficients $D_j^{\alpha\beta}$ and $C_j^{\alpha\beta}$ for $\alpha\neq \beta$ vanish in Eq. (\ref{eq:bosonizaion_1}).
Third, the $R_a^{-1}T_{2a}$ symmetry requires
\begin{flalign}
&D_1^{xx}=D_3^{yy}=D_5^{zz}=D_2\nonumber\\
&D_1^{yy}=D_3^{zz}=D_5^{xx}=D_3\nonumber\\
&D_1^{zz}=D_3^{xx}=D_5^{yy}=D_1\nonumber\\
&D_2^{xx}=D_4^{yy}=D_6^{zz}=D_2^\prime \nonumber\\
&D_2^{yy}=D_4^{zz}=D_6^{xx}=D_1^\prime\nonumber\\
&D_2^{zz}=D_4^{xx}=D_6^{yy}=D_3^\prime.
\end{flalign}
Fourth, the $R_II$ symmetry requires
\begin{eqnarray}} \def\eea{\end{eqnarray}
D_2=D_3,~D_2^\prime=D_3^\prime.
\eea
Similar relations hold for the $C_j^{\alpha\beta}$'s coefficients.

In summary, the nonsymmorphic nonabelian bosonization formulas are
\begin{eqnarray}} \def\eea{\end{eqnarray}
S_{1+6n}^x&=&D_2 (J_L^x+J_R^x)-C_2 N^x,\nonumber\\
S_{1+6n}^y&=&D_2 (J_L^y+J_R^y)-C_2 N^y,\nonumber\\
S_{1+6n}^z&=&D_1 (J_L^z+J_R^z)-C_1 N^z,
\label{eq:bosonize_1}
\eea
\begin{eqnarray}} \def\eea{\end{eqnarray}
S_{2+6n}^x&=&D_2^\prime (J_L^x+J_R^x)+C_2^\prime N^x,\nonumber\\
S_{2+6n}^y&=&D_1^\prime (J_L^y+J_R^y)+C_1^\prime N^y,\nonumber\\
S_{2+6n}^z&=&D_2^\prime (J_L^z+J_R^z)+C_2^\prime N^z,
\label{eq:bosonize_2}
\eea
\begin{eqnarray}} \def\eea{\end{eqnarray}
S_{3+6n}^x&=&D_1 (J_L^x+J_R^x)-C_1 N^x,\nonumber\\
S_{3+6n}^y&=&D_2 (J_L^y+J_R^y)-C_2 N^y,\nonumber\\
S_{3+6n}^z&=&D_2 (J_L^z+J_R^z)-C_2 N^z,
\label{eq:bosonize_3}
\eea
\begin{eqnarray}} \def\eea{\end{eqnarray}
S_{4+6n}^x&=&D_2^\prime (J_L^x+J_R^x)+C_2^\prime N^x,\nonumber\\
S_{4+6n}^y&=&D_2^\prime (J_L^y+J_R^y)+C_2^\prime N^y,\nonumber\\
S_{4+6n}^z&=&D_1^\prime (J_L^z+J_R^z)+C_1^\prime N^z,
\label{eq:bosonize_4}
\eea
\begin{eqnarray}} \def\eea{\end{eqnarray}
S_{5+6n}^x&=&D_2 (J_L^x+J_R^x)-C_2 N^x,\nonumber\\
S_{5+6n}^y&=&D_1 (J_L^y+J_R^y)-C_1 N^y,\nonumber\\
S_{5+6n}^z&=&D_2 (J_L^z+J_R^z)-C_2 N^z,
\label{eq:bosonize_5}
\eea
\begin{eqnarray}} \def\eea{\end{eqnarray}
S_{6+6n}^x&=&D_1^\prime (J_L^x+J_R^x)+C_1^\prime N^x,\nonumber\\
S_{6+6n}^y&=&D_2^\prime (J_L^y+J_R^y)+C_2^\prime N^y,\nonumber\\
S_{6+6n}^z&=&D_2^\prime (J_L^z+J_R^z)+C_2^\prime N^z,
\label{eq:bosonize_6}
\eea
in which $J^\alpha_L$, $J_R^\alpha$ and $N^\alpha$ are defined in Eq. (\ref{eq:J_LR}) and Eq. (\ref{eq:epsilon_N}).
With these nonsymmorphic nonabelian bosonization formulas, one can calculate any low energy property of the system using the SU(2)$_1$ WZW model.
We note that the origin of the nonsymmorphic bosonization coefficients $C_i$, $D_i$, $C_i^\prime$, $D_i^\prime$ ($i=1,2$) arise from wavefunction renormalization effects at the ``Planck scale" of the lattice as discussed in Ref. \onlinecite{Yang2020c}.

\section{Numerical results}
\label{sec:numerics}

In this section, we present the numerical evidence for the emergent SU(2)$_1$ conformal symmetry in the 1D spin-1/2 Kitaev-Gamma-DM  model.
Throughout this section, we use the following parametrization,
\begin{eqnarray}} \def\eea{\end{eqnarray}
K&=&\cos(\theta),\nonumber\\
\Gamma&=&\sin(\theta),\nonumber\\
D_M&=&D_M.
\label{eq:new_parametrization}
\eea
We will numerically study the region $K<0$, $\Gamma<0$, which corresponds to the unitarily equivalent (under $R(\hat{z},\pi)$ in the original frame) region of ``Emergent SU(2)$_1$ I" in the back half of the sphere in Fig. \ref{fig:phase_KGDM}.
DMRG numerical simulations are performed in the six-sublattice rotated frame defined in Eq. (\ref{eq:6rotation}).

\subsection{Correlation functions}
\label{subsec:correlation}

\begin{figure}[ht]
\begin{center}
\includegraphics[width=7cm]{correlation.pdf}
\caption{Averaged correlation function $\frac{1}{3}\sum_{\alpha=x,y,z} S^{\alpha\alpha}_\pi(r)$ as a function of $r_L=\frac{L}{\pi}\sin(\frac{\pi r}{L})$ on a log-log scale.
DMRG numerics are performed on a system of $L=144$ sites with periodic boundary conditions where the bond dimension $m$ and truncation error $\epsilon$ are take as $m=1200$ and $\epsilon=10^{-9}$.
The parameters in Eq. (\ref{eq:new_parametrization}) are taken as $\theta=1.15\pi$, $D_M=0.3$.
}
\label{fig:correlation}
\end{center}
\end{figure}

\begin{figure}[ht]
\begin{center}
\includegraphics[width=7cm]{log_correction.pdf}
\caption{
$[\frac{1}{3}\sum_\alpha S^{\alpha\alpha}_\pi(r)\cdot r_L]^2$ as a function of $\log r_L$ for $J_2=0$ (orange line) and $J_2=0.135$ (blue line).
DMRG numerics are performed on a system of $L=144$ sites with a periodic boundary condition where the bond dimension $m$ and truncation error $\epsilon$ are take as $m=1200$ and $\epsilon=10^{-9}$.
The parameters in Eq. (\ref{eq:new_parametrization}) are taken as $\theta=1.15\pi$, $D_M=0.3$.
}
\label{fig:log_correction}
\end{center}
\end{figure}

First, we study the spin correlation functions.
By properly normalizing the WZW current operators and the primary field, the SU(2)$_1$ WZW model predicts the following static correlation functions,
\begin{eqnarray}} \def\eea{\end{eqnarray}
\langle J^\alpha(0)J^\beta(r)\rangle &=&\delta_{\alpha\beta}\frac{1}{r^2},\nonumber\\
\langle N^\alpha(0)N^\beta(r)\rangle &=&\delta_{\alpha\beta}\frac{(\ln (r/r_0))^{1/2}}{r},
\label{eq:correlation_WZW}
\eea
in which $J^\alpha=J^\alpha_L+J^\alpha_R$;
$\langle ... \rangle$ represent the expectation value over the ground state;
the time variable is taken as zero;
the arguments in $J^\alpha$ and $N^\alpha$ are spatial coordinates;
the logarithmic correction in $\langle N^\alpha(0)N^\beta(r)\rangle$ comes from the marginally irrelevant operator $-u\int \vec{J}_L\cdot \vec{J}_R$ in the low energy theory;
and $r_0$ is an ultraviolet cutoff,
which is of the same order  as the lattice constant.
Using Eq. (\ref{eq:correlation_WZW}) and the nonsymmorphic nonabelian bosonization formulas in Eqs. (\ref{eq:bosonizaion_1}), we obtain
\begin{flalign}
&\langle S^{\alpha}_i S^{\beta}_{j+6n}  \rangle =\nonumber\\
& \delta_{\alpha \beta} \big[ -D_{i}^{\alpha\alpha} D_{j}^{\alpha\alpha}\frac{1}{r^2} +(-)^r C_{i}^{\alpha\alpha} C_{j}^{\alpha\alpha}\frac{\ln^{1/2}(r/r_0)}{r} \big],
\label{eq:modified_correlation}
\end{flalign}
in which $1\leq i,j\leq 6$.
As can be easily seen from Eq. (\ref{eq:modified_correlation}), in the long distance limit $r\gg 1$, the staggered component of the correlation function with the $(-)^r$ oscillating factor dominates over the uniform component.

Fig. \ref{fig:correlation} shows $\frac{1}{3}\sum_{\alpha=x,y,z} S^{\alpha\alpha}_\pi(r)$ as a function of $r_L$ on a log-log scale,
in which  $\theta=1.15\pi$, $D_M=0.3$ defined in Eq. (\ref{eq:new_parametrization});
$S^{\alpha\alpha}_\pi(r)$ is the $\pi$-wavevector oscillating  component of the correlation function $\langle S^{\alpha}_1 S^{\alpha}_{r} \rangle$ as a function of $r$;
$r_L=\frac{L}{\pi}\sin(\frac{\pi r}{L})$ in accordance of CFT in finite size systems \cite{DiFrancesco1997};
and DMRG numerics are performed on a system of $L=144$ sites with periodic boundary conditions where the bond dimension $m$ and truncation error $\epsilon$ are taken as $m=1200$ and $\epsilon=10^{-9}$.
The slope of the line in Fig. \ref{fig:correlation} is extracted to be $-0.935$ by assuming a linear relation,
which is pretty close to $-1$ as predicted by the SU(2)$_1$ CFT.
In fact, the deviation from $-1$ originates from the logarithmic correction in Eq. (\ref{eq:modified_correlation}).

To further study the logarithmic correction, we plot $[\frac{1}{3}\sum_\alpha S^{\alpha\alpha}_\pi(r)\cdot r_L]^2$ as a function of $\log r_L$ as shown by the orange line in Fig. \ref{fig:log_correction}.
It can be observed that the line is linear with a non-vanishing slope, indicating a logarithmic correcting factor with a $1/2$  power in $S^{\alpha\alpha}_\pi(r)$.

In fact, the logarithmic correction can be killed by introducing a second nearest neighbor Heisenberg term \cite{Affleck1988} in the six-sublattice rotated frame.
By introducing a $J_2$ term into Eq. (\ref{eq:Ham_rot}), we consider the following Hamiltonian,
\begin{eqnarray}} \def\eea{\end{eqnarray}
H^\prime_2&=&\sum_{\langle ij \rangle\in\gamma\,\text{bond}}\big(-KS_i^\gamma S_j^\gamma - \Gamma_1 S_i^\alpha S_j^\alpha-\Gamma_2 S_i^\beta S_j^\beta\big),\nonumber\\
&&+J_2\sum_{i} \vec{S}_i\cdot \vec{S}_{i+2}.
\label{eq:Ham_rot2}
\eea
The $J_2$ term renormalizes the coupling constant $u$ in the $\vec{J}_L\cdot \vec{J}_R$ term in Eq. (\ref{eq:low_energy_theory_2}).
When $J_2$ is  at a  critical value $J_{c2}$, the coupling $u$ vanishes and the logarithmic correction is killed.

The blue line in Fig. \ref{fig:log_correction} shows $[\frac{1}{3}\sum_\alpha S^{\alpha\alpha}_\pi(r)\cdot r_L]^2$ as a function of $\log r_L$ when $J_2$ is chosen as $J_2=0.135$.
Clearly, the blue line has a significantly reduced slope compared with the orange line in the same figure,
hinting a critical value  $J_{c2}$ very close to $0.135$.

\subsection{Central charge}
\label{subsec:central_charge}

\begin{figure}[ht]
\begin{center}
\includegraphics[width=7cm]{DM_central_charge2.pdf}
\caption{
$S_L(r)$ as a function of $\frac{1}{3} \ln \left[ \frac{L}{\pi} \sin\left( \frac{\pi r}{L} \right) \right]$ for a variety of $D_M$ at $\theta=1.2\pi$, where the parametrization is defined in Eq. (\ref{eq:new_parametrization}).
DMRG numerics are performed on a system of $L=96$ sites with a periodic boundary condition where the bond dimension $m$ and truncation error $\epsilon$ are taken as $m=1200$ and $\epsilon=10^{-8}$.
}
\label{fig:DM_central_charge2}
\end{center}
\end{figure}

In this subsection, we study the central charge of the system.
SU(2)$_1$ CFT predicts a central charge $c=1$.
We will show the numerical evidence supporting this prediction in the emergent SU(2)$_1$ phase in Fig. \ref{fig:phase_KGDM}.
DMRG numerics are performed on a system of $L=96$ sites with periodic boundary conditions where the bond dimension $m$ and truncation error $\epsilon$ are taken as $m=1200$ and $\epsilon=10^{-8}$.
The parameter $\theta$ in Eq. (\ref{eq:new_parametrization}) is fixed to be $\theta=1.2\pi$, and $D_M$ is tuned.

We compute the entanglement entropy $S_L(x)$ of a subregion $x$ to extract the value of the central charge.
Conformal field theory predicts the following scaling of the entanglement entropy \cite{Calabrese2009}
\begin{align}
    S_L(r) = \frac{c}{3} \ln \left[ \frac{L}{\pi} \sin\left( \frac{\pi r}{L} \right) \right] + \cdots.
    \label{eq:entanglement}
\end{align}
Fig. \ref{fig:DM_central_charge2} shows $S_L(r)$ vs. $\frac{1}{3} \ln \left[ \frac{L}{\pi} \sin\left( \frac{\pi r}{L} \right) \right]$ for a variety of $D_M$ at $\theta=1.2\pi$.
It is clear from Fig. \ref{fig:DM_central_charge2} that the slopes are all very close to $1$, indicating $c=1$ in accordance with Eq. (\ref{eq:entanglement}).

\subsection{Scaling of the finite size gap}
\label{subsec:scaling_gap}

\begin{figure}[ht]
\begin{center}
\includegraphics[width=7cm]{DM_gap_scaling.pdf}
\caption{
Excitation gap as a function of $1/L$  at  $\theta=1.2\pi$, $D_M=1.0$.
}
\label{fig:DM_gap_scaling}
\end{center}
\end{figure}

\begin{figure}[ht]
\begin{center}
\includegraphics[width=7cm]{DM_gap_scaling2.pdf}
\caption{
Excitation gap as a function of $D_M$ with fixed $\theta=1.2\pi$
for several system sizes marked with different colored lines.
}
\label{fig:DM_gap_scaling2}
\end{center}
\end{figure}

In this section, we discuss the scaling of the finite size gap,
which is predicted to be $\sim1/L$ according to CFT.

Fig. \ref{fig:DM_gap_scaling} shows the excitation gap as a function of $1/L$ at $\theta=1.2\pi$, $D_M=1.0$,
which is clearly very linear, consistent with the CFT prediction.

Fig. \ref{fig:DM_gap_scaling2} shows the scaling of the gap by tuning $D_M$ where $\theta$ is fixed as $\theta=1.2\pi$.
As can be seen from Fig. \ref{fig:DM_gap_scaling2}, the range of the emergent SU(2)$_1$ phase is rather large,
except the narrow region for $D_M\in [1.68,1.80]$ where the $1/L$ scaling fails.
We expect the regions for $D_M\leq 1.68$ and $D_M\geq 1.80$ in Fig. \ref{fig:DM_gap_scaling2} to lie in the unitarily equivalent (under $R(\hat{z},\pi)$ in the original frame) counterparts   of the ``Emergent SU(2)$_1$ I" and ``Emergent SU(2)$_1$ II" phases in Fig. \ref{fig:phase_KGDM}, respectively, in the back half of the unit sphere.

\subsection{Phase transitions}
\label{subsec:phase_transition}

\begin{figure*}[ht]
\begin{center}
\includegraphics[width=18cm]{DM_phase_transition.pdf}
\caption{(a) Ground state energy per site  $E_{gs}/L$, (b) first order derivative $\frac{1}{L}\frac{\partial E_{gs}}{\partial D_M}$,
(c) second order derivative $\frac{1}{L}\frac{\partial^2 E_{gs}}{\partial D_M^2}$ as functions of $D_M$ for $L=18$ (black), $L=36$ (red) and $L=72$ (green) at  $\theta=1.2\pi$.
}
\label{fig:DM_phase_transition}
\end{center}
\end{figure*}

In this subsection, we take a closer look at the region $D_M\in [1.68,1.80]$ in Fig. \ref{fig:DM_gap_scaling2}, where the system does not show a Luttinger liquid behavior.

Fig. \ref{fig:DM_phase_transition} (a), (b), (c) show the ground state energy per site  $E_{gs}/L$, the first order derivative $\frac{1}{L}\frac{\partial E_{gs}}{\partial D_M}$,
and the second order derivative $\frac{1}{L}\frac{\partial^2 E_{gs}}{\partial D_M^2}$, respectively, as functions of $D_M$, at $\theta=1.2\pi$.
Interestingly, there seems to be several different phases in the narrow region $D_M\in [1.68,1.80]$, which separates the two emergent SU(2)$_1$ phases.
More investigations on the physics in this narrow region will be left for future studies.

\section{Summary}
\label{sec:summary}

In summary, we have studied the spin-1/2 Kitaev-Gamma chain with a bond-dependent Dzyaloshinskii-Moriya interaction.
Using a two-site periodic unitary transformation which maps the Gamma and Dzyaloshinskii-Moriya terms into one another, the phase diagram of a pure Kitaev chain with a Dzyaloshinskii-Moriya term is obtained from the known results of the Kitaev-Gamma model.
More importantly, we are able to analytically demonstrate that there is an extended gapless phase in the phase diagram of the spin-1/2 Kitaev-Gamma chain with a nonzero Dzyaloshinskii-Moriya interaction,
and such gapless phase has an emergent SU(2)$_1$ conformal symmetry at low energies.
The analytical predictions are supported by density matrix renormalization group simulations.
Our work is useful to understand the effects of the  Dzyaloshinskii-Moriya interactions and the electric fields in one-dimensional and quasi-one-dimensional generalized Kitaev spin models.

\begin{acknowledgments}
W.Y. and I.A. acknowledge support from NSERC Discovery Grant 04033-2016.
C.X. is partially supported by Strategic Priority Research Program of CAS (No. XDB28000000).
A.N. acknowledges computational resources and services provided by Compute Canada and Advanced Research Computing at the University of
British Columbia. A.N. acknowledges support from the Max Planck-UBC-UTokyo Center for Quantum Materials and the Canada First Research Excellence Fund
(CFREF) Quantum Materials and Future Technologies Program of the Stewart Blusson Quantum Matter Institute (SBQMI).
\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


text:
Chhudzom Gewog (Dzongkha: ཆུ་འཛོམས་) is a gewog (village block) of Sarpang District, Bhutan.

References

Gewogs of Bhutan
Sarpang District

redpajama_set_name: RedPajamaWikipedia


In my current project, we make use of numerous different Word templates, but the basic for them all is they have a header and footer and they are the same. Header and footer containing quick-party showing SharePoint metadata, for e.g. status of the document. Of cause the values must be updated if the user changes them either from Word (document information panel) or from the SharePoint UI. We made a lot of templates, from meeting minutes to a letter template and all the values from the quick-party fields updated fine but our most simple Word template that only contain, header and footer, did not work. After a very long search we came to the Word template must include a text and a space is enough.
I got a request from a customer, where they needed to add a custom address field to the head in a Word template. The address list need to come from a single source and easy to by update.
Create the custom address list in SharePoint. Need a multiline field, where the address with line breaks can be added.
Add value to the list.
I call my content type "Letter".
Add multiline text field, to the content type. In my demo i use the build in field Address.
When done, the content type look like this. Click on the document infomartion panel settings link.
Clikc on the "Create a new custom template" link.
When InfoPath is finish loading, click on the "show field" button in the ribbon, "manage data connection" and then "Add…".
Follow the data connection wizzard.
The locatition is the url to the SharePoint site where the custom address list is created.
The done, the new data connection is add to the data connection lists.
Right click on the Address field textbox, select "Change Control" and select "Drop-Down List Box".
Click on the Address field and select Drop-Down List Box Properties.
Change the properties to look like this.
Remove the line break after the first horizontal region.
Click on the Quick Publish button, in the right top corner.
InfoPath will akes if you want to save the InfoPath template, before publish it.
On the document library, go to the document library settings page and under the "Advanced settings" page, change the setting "Allow management of content types" to true.
And the "Letter" content type.
Go back to the document library and create a document based on the content type. This is the easyed way to create a template with the proper field add to the Word template.
Then Word is finish loading, go to the backstage, by clicking on the "file" icon, then click on the "properties" and select "Show Document Panel".
In my demo, i edit the header. Go the Ribbon, under the "Insert" tab, select "Quick Part", "Document Property" and then the "Address" field.
My template ends up looking like this.
Save the document as a "dotx" file (Word template file).
Find the "Letter" content type, select the "Advanced settings".
Upload the template og click on the "OK" button.
Go back to the document libary, click on the "Letter" content type in the "new document" button in the Ribbon.
Select the address in the document infomation panel.
I release the SharePoint Manager 2013 some time ago, more precisely on Jul 19 2012 and it now has over 2500 downloads on CodePlex witch I think is very good. This version is only intend as an upgrade of the 2010 version. However, I has added two new features. Both based on the feedback that has come from the 2010 version about speed. The first function is the most visual of the two. Function is plain and simply a splash screen that displays a picture as soon as you start the SharePoint Manager. The second feature is a configuration value in app.config file. The function is called "ShallowExpand". Set it to true and the next time you start the SharePoint Manager only loads the farm and webapplication objects into treeview.


Local Private Tour Guide | Sao Paulo, Brazil | Gilbran C.
About me: I have graduated in Social Communication from Pontifícia Universidade Católica Rio de Janeiro and Theater by Casa de Artes de Laranjeiras.
For ten years I have been working for several tourism companies in the cities of São Paulo and Rio de Janeiro, as Private Tourism Guide. I also act as a private translator of English and Spanish in business meetings, fairs, and events.
Previously I have also worked in hospitality industry for eleven years as Operations Manager at Holiday Inn World Wide (now InterContinental Hotels Group) and Utell International, both in call centers.
I have lived in the United States for two years where I have studied at Camarillo High School and at Ventura City College.
My knowledge of Arts, Architecture, and History of São Paulo was acquired over the years for having a family related to art and museums, from my studies in those institutions and by self-learning.
The tours will demonstrate a quick and objective panorama of the best or most significant places, monuments and attractions of São Paulo.
You will get a local look not only on the physical architectural aspect, but you will understand its evolution, dynamics, high points, discrepancies and differences.
At the end of the tour you will feel like you are already part of the city!
We had a wonderful day with Gil. He gave us a very informative talk about the history of Brazil, as well as giving us a comprehensive tour of the ups and downs of São Paulo. Great tour and guide , would highly recommended. We felt safe and and comfortable in his very capable hands.


text:
Myomyscus est un genre de rongeurs de la sous-famille des Murinés.

Liste des espèces
Ce genre comprend les espèces suivantes selon Mammal Species of the World :

Myomyscus angolensis Bocage, 1890
Myomyscus brockmani Thomas, 1908
Myomyscus verreauxii Smith, 1834
Myomyscus yemeni Sanborn and Hoogstraal, 1953

Référence

Shortridge, 1942 : Field notes on the first and second expedition of the Cape Museum's mammal survey of the Cape Province and descriptions of some new subgenera and subspecies. Annals of the South African Museum 36 pp 27-100.

Liens externes

Rongeur (nom scientifique)
Muridae


text:
Aaron Lane Cook (born February 8, 1979) is an American former professional baseball pitcher. He played in Major League Baseball (MLB) for the Colorado Rockies and Boston Red Sox.

High school
In high school, while playing for Hamilton High School (Hamilton, OH), Cook allowed only one home run, to fellow Major Leaguer Kevin Youkilis, who was playing for Sycamore High School in suburban Cincinnati.

Colorado Rockies
Cook was drafted by the Colorado Rockies in the second round of the 1997 MLB Draft and made his Major League debut in 2002.

2002 season
Cook made his debut, against the Chicago Cubs, pitching two innings and allowing a home run. He would make his first start, against the San Francisco Giants, pitching six innings while allowing four walks in a no decision. Cook would finish the season appearing in nine games (five starts) with a 4.54 ERA in 35 innings.

2003 season
Cook made the opening day roster after pitching a solid spring training and was named the Rockies' #2 starter, opening the season against the Houston Astros.

After posting an ERA of over 5.00 through 14 starts, Cook was demoted to Triple A in exchange for Denny Neagle, who had come out of his rehab assignment.

Cook would finish the season 4–6 with a 6.02 ERA in 124 innings. He also allowed 57 walks to 43 strikeouts.

2004 season
Cook saw his 2004 season come to an abrupt end when it was discovered that he suffers from pulmonary embolism, or blood clots. During an August 7 start against the Cincinnati Reds, Cook complained of dizziness and shortness of breath. After he was taken to a local hospital, doctors discovered blood clots had formed in his right shoulder. On September 10, Cook underwent extensive surgery at a St. Louis hospital, during which the first rib on his right side was removed to relieve compression on a major blood vein.

His season was cut short due to this injury, finishing with just 16 starts and a 6–4 record.

2005 season

Cook stayed on the disabled list until July 30, when he gave up seven runs and eleven hits in 4 innings of a 9–2 loss to the Philadelphia Phillies at Coors Field. His first 2005 victory came in an 11-2 decision over the Milwaukee Brewers on August 15, when he pitched six innings and gave up two runs and nine hits. In his final 12 starts of 2005, Cook went 7–1 with a 3.07 ERA. For this outstanding recovery from his very serious condition, he was awarded the 2005 Tony Conigliaro Award.

2006 season
After battling numerous injuries and inconsistency during his first three years, Cook stayed in the rotation throughout the season, posting an ERA of 4.23 in 32 starts for the Rockies, finishing 9–15. He had 92 strikeouts in 212 innings.

Despite pitching half his games in Coors Field, Cook's ERA was a run higher on the road (4.62) than at home (3.96).

2007 season
On June 28, 2007, Cook allowed Craig Biggio's 3,000th hit in Minute Maid Park.

Cook missed nearly two months with a strained side muscle, missing the first two rounds of the playoffs, yet, Cook managed to pitch in the World Series.

He pitched in the last game of the World Series against the Boston Red Sox, pitching six innings while allowing three runs and having two strikeouts. The Rockies did not catch up and ultimately lost, swept in the process.

Cook finished the season with an 8–7 record in 25 starts. After the 2007 season, $4.5 million next year under an option the Rockies exercised and Cook signed a three-year contract extension worth a guaranteed $30 million and a team option for the 2012 season.

2008 season

Cook won six consecutive starts from April 13, 2008, to May 9, 2008.  He is one of only four Rockies pitchers to have won 11 games before the All Star break through 2010; the only others are Shawn Chacón (2003) Jason Marquis (2009)and Ubaldo Jiménez (2010).

On July 6, 2008, Cook was named an All-Star to the 2008 Major League Baseball All-Star Game. The All-Star selection was the first of his career.  He pitched three scoreless innings in the All-Star Game, and at one point pitched out of a no-out, bases loaded jam after two errors and an intentional walk, avoiding the loss. Various broadcasters have stated that, had the National League won the game, he would have been named MVP of the All-Star Game that year.

In a 2008 game against the San Diego Padres, Cook threw a complete game shutout while hurling just 79 pitches.

Cook finished the 2008 season with a career high 16 wins and 96 strikeouts. He gave up 20 hits on 0-2 counts, more than any other pitcher in baseball.

2009 season
Cook was close to following his 2008 campaign with another good season for the Rockies, compiling a record of 10-6 through the month of August until an injury caused him to miss the month of September. Cook would later appear in October, pitching eight innings in a win over the Milwaukee Brewers.

Cook pitched in the first round of the playoffs against the Phillies, pitching five innings and allowing three runs in a 5–4 victory. The Rockies ultimately lost the series.

2010 season
Cook's 2010 season was a season filled with inconsistency and injuries, as he twice wound up  on the DL. The first of these appearances occurred in August, when Cook landed on the 15‑day disabled list with a sprained toe.

Cook  came back in September; after pitching in just his second start off the disabled list, Cook suffered a non displaced fracture in his leg, ending his 2010 season.

Cook ended his season on a disappointing note, finishing 6–8 with an ERA of 5.08 in 23 starts.

2011 season
Cook's season was cut short for the third straight time, as he finished with a 3–10 record and a 6.03 ERA in 18 games (17 starts) and was let go after the season,  the team declining his $11 million option.

Boston Red Sox

2012 season

On January 14, 2012, Cook signed a minor league deal with the Boston Red Sox that included an opt-out clause if he did not make the Red Sox by May 1. Cook was recovering from shoulder and knee injuries that plagued him in 2010 and 2011. In five games with Triple-A Pawtucket, he went 3–0 with two complete games. On May 1, the day he chose to exercise his opt-out clause, it was announced he would be promoted to Boston to start in place of the injured Josh Beckett. Cook received a pro-rated salary of $1.5 million plus incentives. He also had a second opt-out clause for June 1.

On May 5, 2012, Cook made his Red Sox debut against the Baltimore Orioles. He pitched only 2 innings, as a result of an injured knee off the spikes of Orioles first baseman Chris Davis. After getting treatment in the clubhouse, Cook returned, only to then allow a two-run home run to Adam Jones. He was placed on the disabled list the next day.

On June 29, 2012, against the Seattle Mariners, Cook threw a complete game shutout, allowing just two hits and walking none over 81 pitches, notching the 74th victory of his career.

Cook would struggle for the rest of the season, finishing with a 4–11 record and a 5.65 ERA. It was his third consecutive season having an ERA over 5.00, following five seasons of maintaining one under 4.25. He also had a K/9 of 1.9, the lowest of any starter with at least 85 innings of work in the Major Leagues.

Philadelphia Phillies
On January 16, 2013, Cook signed a minor league deal with an invitation to spring training with the Philadelphia Phillies. He was released by the Phillies on March 26, 2013, as he did not make the big league roster.

Colorado Rockies (minor leagues)
On March 29, 2013, Cook signed with the Colorado Rockies. He signed to play with Colorado Springs Sky Sox, the Rockies Triple A Baseball team.
 After posting a 0–5 record with an 8.15 ERA, Cook told the team on July 19 that he would not pitch for them again in 2013, and was released. It was later revealed Cook had severe inflammation in his elbow, and decided to end his season.

2014 season
After missing most of the 2013 season due to injury, Cook after more than five months expressed a desire to return to pitching. Cook later decided to rest and work out for MLB teams in 2015.

Pitching style
Cook is a sinkerballer. Cook relies on a heavy sinker, which he throws more than 70% of the time and induces ground balls at an average 64% of the time. His sinker is considered by many hitters like trying to hit an anvil falling, as it bottoms out at the end. His response to his style of pitching has always been: "I'm a pitch to contact guy, I may not be a flashy pitcher because I don't get the K's. I work quick and I make hitters make contact on my sinker and induce the ground ball".

His repertoire also includes a curveball, a changeup and a cutter he added in 2010.

See also

 List of Colorado Rockies team records

References

External links

1979 births
Living people
Colorado Rockies players
Boston Red Sox players
Major League Baseball pitchers
Baseball players from Kentucky
National League All-Stars
Arizona League Rockies players
Portland Rockies players
Asheville Tourists players
Salem Avalanche players
Carolina Mudcats players
Colorado Springs Sky Sox players
Tri-City Dust Devils players
Modesto Nuts players
Tulsa Drillers players
Pawtucket Red Sox players


text:
Unmanned Systems Australia part of Google [X] Project Wing
August 29, 2014 Editor
Unmanned Systems Australia is proud to announce its partnership with Google [X] as part of Project Wing. The Google [X] project has been running for two years and is designed to develop self flying vehicles as part of an aerial delivery system. Unmanned Systems Australia trained on the Project Wing vehicle and was granted by CASA a Unmanned Operating Certificate to enable the delivery services to be tested. Unmanned Systems Australia and staff from Project Wing work closely with CASA throughout this unique project to gain all of the necessary approvals.
Channel 7 Media Interview
Media Article IT News
Migrant Offshore Aid Station (MOAS) sets off with Schiebel UAS on board
The Migrant Offshore Aid Station (MOAS), which is the first ever privately-funded migrant aid station, will set off on the first of a number of missions on Wednesday after two days of sea trials.
However, even before the proper mission started, the Phoenix 1 has already carried out its first rescue mission. The boat was heading to an area to pick up supplies when it came upon a small fishing boat drifting in the water. The engine had stopped working and the fisherman, who had his five-year-old son with him, was getting worried. The man's boat was tied up alongside the MOAS ship until help arrived.
S100 CAMCOPTER on board the MOAS in MALTA
Courtesy: The Malta Independent.
Commercial UAS Application, Unmanned Surface Vessels, Unmanned Systems, Unmanned Underwater Vehicles
UNMANNED SYSTEMS AUSTRALIA ANNOUNCES A JOINT VENTURE WITH UVS TO MARKET MARITIME UNMANNED SYSTEMS
Brisbane Australia, 27 August 2014 – Unmanned Systems Australia announces that it has agreed with UVS to jointly market Maritime Unmanned Systems. Unmanned Systems Australia Pty Ltd is a UAS consulting and training services company that assist companies understand and enter the Unmanned Systems market. The joint marketing of unmanned maritime systems is the first of many jointly marketed products by Unmanned Systems Australia designed to help companies market their products to a growing unmanned systems environment across various domains.
The Unmanned Systems market in Australia is experiencing a significant growth with over 130 certified commercial Unmanned Aerial operators in Australia. The growth in the Australian market for unmanned systems has almost doubled since Jan 2014.
Unmanned Systems Australia and UVS believe that the combination of both airborne and maritime surface and sub-surface unmanned autonomous systems is a significant step forward in developing a combined maritime littoral autonomous unmanned system.
"Australia has one of the longest coastlines in the world, and significant environmental and natural resources in the waters off the coast of Australia. Fisheries compliance, border security, coastal erosion, shark monitoring, water quality monitoring and hydrography can be greatly enhanced by the combination of both maritime and airborne systems working together" states Phil Swinsburg, Managing Director of Unmanned Systems Australia.
Phil Swinsburg says that "the joint marketing of unmanned maritime systems is the first step in a broadening number of solutions being offered to future clients. We are also expanding our airborne unmanned system companies that we partner with to provide a turn-key package to meet a wide variety of precision agricultural, infrastructure monitoring, environmental monitoring and emergency response solutions. We will assist companies in their approvals process with the Civil Aviation Safety Authority and provide OEM training and in-country support".
UVS provides an experienced unmanned maritime systems support capability in Australia through offices located in Newcastle, Melbourne and Perth. In the Defence market UVS supports the Royal Australian Navy (RAN) fleet of six Liquid Robotics' Wave Glider vehicles and the REMUS Autonomous Unmanned Vehicles (AUV) operated by DSTO and Navy. In Offshore Oil & Gas UVS has extensive experience in AUVs for survey applications and ROV support including specification and sale of subsea components such as cameras, sonars, lights and connectors. The UVS engineering capability is often used by customers for application engineering and for integration of new components and payloads into ROVs and AUVs.
The Liquid Robotics Wave Glider represents an innovative new capability for instrumenting the ocean. Powered by wave action alone, the Wave Glider is capable of autonomous operation for missions in the ocean of many months. Two Wave Glider vehicles have proven the endurance of the Wave Glider by completing a 9,000 nautical mile scientific journey across the Pacific Ocean to set a new world record for the longest distance travelled by an autonomous vehicle. Applications for Wave Gliders include Meteorological Data, Security and Border Patrol, Gateway for AUVs, Environmental and Geophysical monitoring.
Both Unmanned Systems Australia and UVS believe that the combination of aerial and maritime surface and sub-surface vessels working together unlocks a significant increase in potential for unmanned autonomous systems to support maritime applications.
About Unmanned Systems Australia:
Unmanned Systems Australia Pty Ltd is a UAS Consulting Company with over 20 years' experience in operating Unmanned Systems and has been focusing on the commercial and civil UAS marketplace since 2008. Unmanned Systems Australia provides a turn-key solution through their UAS Business Solutions for companies and government agencies seeking to enter the unmanned market for commercial purposes. A growing list of partnered aircraft companies provide a menu of systems available for selection tailored to the commercial market. OEM training and after sales support is also provided.
Unmanned Systems Australia Pty Ltd ABN: 48129675770, CASA UOC License number 1-11LN0P-01, CASA Safety Consultant License Number 06/829-26.
For more information see: www.unmannedsystemsaustralia.com.au
About UVS:
UVS Pty Ltd has a history of ocean engineering excellence which dates back to the early 1980s. In Australia, UVS Pty Ltd is the exclusive representative for many of the world's leading marine technology manufacturers. UVS capabilities are extremely comprehensive, specialising in sales, support and custom engineering to service clients in offshore oil & gas, naval defence, oceanography, hydrographic survey, underwater communications, geophysical exploration, autonomous and remotely operated vehicles and many other complex marine applications. UVS has always been at the forefront of introducing new and innovative technologies to the region and the Liquid Robotics Wave Glider is the latest example of this philosophy.
UVS Pty Ltd A.B.N 97 150 810 898
For More Information see: http://www.uvs.com.au/
MARITIME UNMANNED SYSTEMSNAVYNavy UASUnmanned Systems AustraliaUVS

redpajama_set_name: RedPajamaCommonCrawl


text:
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redpajama_set_name: RedPajamaGithub


Special Agents with the NPS Investigative Services Branch Atlantic Field Office are attempting to identify persons of interest in Knoxville and eastern Tennessee areas.
The persons listed are believed to have information about, or may have witnessed, a sexual assault that occurred in Great Smoky Mountains National Park.
If you can help identify these persons of interest, please contact the National Park Service Investigative Services Branch - and remember, you don't have to tell us who you are, but please tell us what you know.


text:
Creators Going Pro: Meet Brittany Null, The YouTube Supermom Whose Channel Is A 10-Year Chronicle Of Her Life
By James Hale
Welcome to Creators Going Pro, where in partnership with Semaphore — a creator-focused family of companies providing business and financial services to social media professionals — we profile professional YouTube stars who have hit it big by doing what they love. Each week, we'll chat with a creator about the business side of their channel, including identifying their Semaphore Moment — the moment they truly went pro.
For the past decade, Brittany Null has shared everything with her viewers. She originally started her YouTube channel, Britt's Space, as a hobby, something she used as a kind of digital diary. Her earliest videos are near-daily detailings of the everyday goings-on in her life. They're frank, lo-fi chronicles of short road trips, her relationships with her then-spouse and family members, and the occasional skit and storytime. And while lots has changed in the years she's been a creator, including the addition of three little ones to her family and a gathering of 393K subscribers, there's one thing that hasn't: the core of her content.
Null's videos, though they're now more slickly produced and often sponsored by big brands like IKEA, Target, and Disney, still depict her everyday life. And, by the numbers, it's clear viewers are still here for it. Her most-viewed videos, generally netting between 30K and 40K views each (she garners around 200K views per month total), are consistently her life update vlogs, where she sits down, often one-on-one with the camera, and details what's been happening in her life. She doesn't shy away from discussing subjects other folks could find tricky or too personal to talk about — subjects like ending a marriage, what it's really like to coparent (below), and dealing with anxiety.
That's not to say Null's content is all about what's going on in life outside the internet, however. She also costars with her kids in plenty of trendy videos, things like gift reveal videos and taste tests and vacation vlogs (below). Her kids have naturally become an integral part of her channel, and that's presented its own set of challenges for her as a creator. She's sensitive about how much time her kids spend on camera, and says she's always made it clear that while YouTube (and all that comes with it, including negotiating brand partnerships and figuring out the financials of AdSense income) is her full-time career, it isn't her kids'.
That belief is evident in Null's upcoming content plans. She's planning to keep making family vlogs, but also wants to start zeroing in on the other types of content she curates, like advice videos, home decor, cooking, and self-care videos.
One thing is obvious: no matter what direction she takes her content, her dedicated viewers will follow right along with her. Check out our chat with her below.
Tubefilter: So first, tell us a little about you and your family! Where are you from? What did you do in the days before YouTube?
Brittany Null: Hey! My name is Britt Null, and in addition to being a digital content creator, I'm a mom to three cuties. I've been creating online content for 10 years. Before YouTube, I was a teacher! Might go back som day, but not too sure, lol.
Tubefilter: You've been on YouTube for nearly a decade now. What made you choose this platform as the place to share your content? What do you think it offers you, as a content creator, to help you grow your platform and build your career?
BN: I originally began creating YouTube content as a fun hobby. Over the years, it grew into a community and business. I think it offers an amazing space to share creative projects, impact and rally for a cause, and also just create content that others can identify with. I've gained an amazing group of followers who have become an online family. They've watched my kids grow, and have been there with me through a lot of life's ups and downs.
As far as growing my content and career, YouTube has connected me to numerous brands and amazing partnerships.
Tubefilter: Tell us about some of your brand partnerships!
BN: I've been blessed to partner with some amazing brands that fit really well into my videos because they're products I already use. I've partnered with IKEA, Target, JCPenney, Sephora, Walmart, Intel, and Disney, to name a few.
Tubefilter: How has your content evolved over time, from your very first videos to the vlogs you make with your kids now?
BN: My content has evolved so much! Now, as a single mama of three, my content reflects more of my personality and interests. I enjoy creating videos with my kids, but have also expanded my videos into other areas, like advice videos, home decor, cooking, and self-care. I'm so grateful for an audience who has kept an open mind and been supportive with all the changes my channel has seen over these past 10 years.
Tubefilter: When did you get your first check for online video revenue? How much was it for?
BN: First check? Wow! So long ago, I'm not sure I remember, but I think it was 2012. And it wasn't much. I remember thinking, "Oh cool! A check! Never even thought we'd make a dime!"
Tubefilter: How does YouTube factor in to you and your kids' daily life? What's your day-to-day schedule like?
BN: As my kids have gotten older, I've tried to make YouTube a fun and seamless aspect of their life. I want them to be a part of it, but also realize it's Mom's job, not theirs. Day to day, I'll film small portions of what's going on. Sometimes they have a lot to share, and sometimes they're not interested in filming anything. I do my best to always respect their wishes. When we have a family project or partnership that requires everyone to be in a video, I make it fun and film it in sections so it doesn't feel overwhelming.
Tubefilter: What was that Semaphore Moment for you—the first time you realized you were a professional creator?
BN: I think it was the year I hired Semaphore to help with the money side of things! LOL. In the beginning, it was just a hobby, and the payment wasn't much. But as the channel grew and partnerships started flowing in, it was surprisingly overwhelming. In 2015 (I think 😬), Semaphore walked in and saved the day!
Tubefilter: What are the challenges of running a channel where your kiddos are stars right alongside you?
BN: I think some of the challenges are being aware of what I share, and also being aware of when to film and when to put the camera away. It's fun to share parts of our lives, but there's also large portions of our lives I enjoy keeping private. I never want my kids to feel like they live their lives with a camera constantly filming their every move. Balance can be tricky at times.
Tubefilter: What makes you love creating content on YouTube?
BN: I enjoy storytelling! Whether it's storytelling about my day or life, or storytelling for a brand, I love creating videos my audience connect to. Videos that are entertaining, relatable, and a space where, for just a moment, even if it's only 10 minutes, the viewer can take a break from life and be encouraged.
Tubefilter: How long does it take you, on average, to put together a video, from scripting to filming to uploading?
BN: On average, putting together a video from start to finish can take multiple days. For a blog-style video that features our week and activities, I usually plan to film a little each day, and then edit the content in one go, which can take two to three hours depending on how much "extra" I add in editing. For sponsored content or videos for a series, I usually brainstorm the general idea, film the content, and then break up the editing into multiple sessions.
Tubefilter: You mentioned working with Semaphore for your financial needs. Who else do you have working with you behind the scenes?
BN: It's a one-women show for me. I film, edit, and manage everything. Occasionally I'll hire my friend to help me film specific projects that need an extra hand, but for the most part, it's just me (and my kids and whoever else I'm filming with for that particular video).
Tubefilter: What do you think is the most vital skill you possess as a creator?
BN: The most vital skill I possess as a creator is my resilience. The online creator world can be a scary space. It's difficult to stay creative, engaged, and also motivated. Being resilient has allowed me to keep going even when things have been hard, and to understand that sometimes you need a break, but needing a break doesn't mean you have to give up.
Tubefilter: What's next for you and your channel? What are you building toward?
BN: I'm building toward creating consistent content that reflects more of who I've become. As much as I love having a "family vlog" channel, I'm moving away from videos that are solely family vlogs to more curated content. I'm so grateful for this space and community, and excited to continue creating!
Semaphore Business Solutions provides customized services for clients across the country, taking an all-encompassing approach to meet all your financial needs. Whether you're a veteran YouTube entertainer or just starting out, managing your business correctly is crucial to avoiding major headaches down the road. The sooner you call us, the sooner we can help you put a plan into motion to grow, as well as to keep more money in your pocket, with advanced tax strategies. Semaphore Brand Solutions has established itself as a leading influencer marketing agency representing our exclusive talent relationships and services to the most recognized brands and agencies.
Creators Going Pro: One YouTube Video Netted ParkerGames $50 In AdSense Revenue — Oh, And His Own Television Show
Creators Going Pro: Kofi McCalla Curates "The Cool Kids' Guide" To Streetwear Around The World
Creators Going Pro: Music-Focused Video Essayist Noah Lefevre Has Built A Career On YouTube Despite The "Daily Struggle" To Keep His Content Monetized


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High-SPF Sunscreens: Are They Better?
https://www.webmd.com/healthy-beauty/features/high-spf-sunscreens-are-they-better
By Salynn Boyles
WebMD Feature
Reviewed by Louise Chang, MD
If you've shopped for sunscreen lately, you have probably noticed the proliferation of products with ever-higher sun protection factor (SPF) ratings.
Just a few years ago, it was hard to find a sunscreen claiming an SPF higher than 45. These days, the shelves are lined with products from companies such as Banana Boat, Coppertone, and Aveeno touting SPF ratings of 70+, 80, and 90+. Neutrogena recently introduced Ultra Sheer Dry-Touch Sunblock SPF 100+. But is a 100+ or a 90+ sunscreen really that much better than one with an SPF of 15?
SPF 100: Twice as Good As SPF 50?
SPF refers to the ability of a sunscreen to block ultraviolet B (UVB) rays, which cause sunburns, but not UVA rays, which are more closely linked to deeper skin damage. Both UVA and UVB contribute to the risk of skin cancer.
It is a measure of the time it would take an individual to burn in the sun if they were not wearing sunscreen vs. the time it would take with sunscreen on.
"SPF is not a consumer-friendly number," says Florida dermatologist and American Academy of Dermatology (AAD) spokesman James M. Spencer, MD. "It is logical for someone to think that an SPF of 30 is twice as good as an SPF of 15, and so on, but that is not how it works."
According to Spencer, an SPF 15 product blocks about 94% of UVB rays, an SPF 30 product blocks 97% of UVB rays, and an SPF 45 product blocks about 98% of rays.
"After that, it just gets silly," he says.
Sunscreens with higher SPF ratings block slightly more UVB rays, but none offers 100% protection.
Spencer says SPF 15 sunscreens are fine if used correctly, but he recommends SPF 30 products to his patients because few people apply sunscreens as heavily or as often as they should.
Farah Ahmed, who is general council for the cosmetics industry group Personal Care Products Council, concedes that the difference in sunburn protection between the medium- and high-SPF sunscreens is not great.
But she says the high SPF products may better protect against long-term skin damage and exposure-related skin cancers.
In a written statement, Neutrogena notes that because most people use far less sunscreen than is recommended, high SPF sunscreens can offer better protection.
"Higher SPFs used over a lifetime may translate to healthier skin in later life," the statement reads. "While the difference in the percentage of ultraviolet radiation blocked between an SPF 55 and SPF 100+ may be slightly less than 1%, applying an SPF 100 may lead to much less cumulative sun damage over a lifetime."
What about UVA Rays?
Finding a sunscreen that adequately protects against UVA rays is much trickier, but every bit as important. UVA radiation reaches deeper into the skin and contributes to wrinkles and skin cancer risk. Nearly all (95%) of the UV radiation that we are exposed to is UVA radiation.


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[January 23, 2023 8:27 pm ET] Qantas Experiences Five Mishaps in One Week
[January 19, 2023 4:00 pm ET] Ethiopian Strengthens U.S. Route Network, Restores Flights to China
[ News ]November 7, 2018 11:24 am ET
By Daniel Morley
Opinion: Airlines Should Charge For Carry-On Bags
In the modern aviation environment, extra fees have become commonplace for passengers. The rise of ultra-low-cost carriers in the United States has seen passengers being charged for everything from assigned seats to their luggage. Even legacy, full-service airlines in the United States have begun offering basic economy fares, in which…
[ News ]September 20, 2018 8:26 pm ET
American and Delta Raise Checked Baggage Fees
American Airlines has decided to increase the fee for the first checked bag from $25 to $30, effective for all tickets purchased September 21 and beyond. The second bag fee will raise from $5 to $40, following a trend that all major carriers, with the exception of Southwest, have recently…
[ News ]August 27, 2018 10:33 pm ET
The Dream Is Over and the Airline Is Awake: JetBlue…
JetBlue Airways has announced a new ancillary fee structure for its passengers, charging more for extra post-booking services such as a checked baggage, change fees, cancellation fees and oversized item fees, among others. The announcement comes just weeks after the airline announced it would downsize its workforce following financial pressure…
[ News ]April 23, 2018 11:46 am ET
IATA Ground Handling Conference Welcomes Delegates to Doha
Sunday night marked the unofficial first day of the IATA's Ground Handling Conference (IGHC), held annually in a different city every year. This year, the city of Doha, Qatar was chosen as the designated city for the conference, the first time the IGHC has been held in Qatar, as well…
[ News ]April 21, 2018 12:00 pm ET
By John Flett
New Report Shows Record Low Number of Mishandled Baggage in…
As previously reported, 2017 was a record year for the aviation industry with the International Air Transport Association (IATA) estimating the number of passengers traveling as 4.02 billion. But this week, it was announced by SITA that 2017 was also a record-setting year for the lowest number of mishandled bags.…
[ News ]March 14, 2018 9:00 pm ET
U.S. Airlines and Their Varying Pet Policies
Following the crackdown on faux emotional support animals and the two United Airlines incidents this past week, it is important that travelers know what to expect when bringing their pets onboard airplanes. For example, did you know that pets can't fly as cargo on many Airbus aircraft due to the…


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Mariusz Woźniak (4 March 1944 – 4 November 2020) was a Polish diplomat, ambassador to Indonesia (1991–1995), Jordan (1999–2003), and Ethiopia (2005–2007).

Life
Woźniak graduated from English studies at the University of Warsaw. In 1981, he started his diplomatic career at the Ministry of Foreign Affairs as expert. He served at the embassies in Washington, D.C. (1981–1982), as First Secretary in Tokyo (1983–1987). Between 1991 and 1995, he represented Poland as ambassador to Indonesia. Next, from 1999 to 2003, he was ambassador to Jordan. Following his short stay at the diplomatic protocol in Warsaw, he ended his career as ambassador in Ethiopia (2005–2007).

Besides Polish, he was speaking English and Russian.

References

1944 births
2020 deaths
Ambassadors of Poland to Ethiopia
Ambassadors of Poland to Indonesia
Ambassadors of Poland to Jordan
University of Warsaw alumni


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Epidemic Prevention Measures
College of Electrical Engineering and Computer Science
College of Applied Sciences
Guide to English-taught Programs
Degree-seeking Students
Inbound Exchange Students
Study in Taiwan
Research at Taiwan Tech
Internationalization at Taiwan Tech
Groundbreaking Ceremony at Taiwan Tech Hsinchu Campus - another milestone for internationalization
The ground breaking ceremony for the extension of Taiwan Tech's new Hsinchu Campus took place on May 13th, 2020, four years after our university had decided to open a new branch campus in Hsinchu, about 70 km northwest of Taipei.
Two new buildings, the International College Building and the Advanced Industrial Cooperation Building, will be constructed on the Taiwan Tech Hsinchu campus. The project, which was delayed by a complicated tendering process and other administrative obstacles, will be completed by June 2022, President Liao Ching-jong said.
"This is an important milestone in Taiwan Tech's internationalization process", Liao explained, "The International College will offer an all-English teaching environment and a foundation-year in liberal arts which will be attractive for international students."
Hsinchu County – which already hosts one of Taiwan's highly successful science parks -, and the nearby town of Zhubei are also expected to benefit from the new Taiwan Tech campus, as several local government officials pointed out in their speeches. "We are looking forward to welcome international students and professors," said Hsinchu County Magistrate Yang Wen-ke, "and we believe that Taiwan Tech's reputation in industry-university cooperation will boost the economic development in our area."
The overall project investment totals about $500 million. The Advanced Industrial Cooperation Building, expected to be completed in May 2021, will host the Industry 4.0 Centre and the New Thin Film Materials Research Centre. The International College Building is planned as a 6-storey clubhouse-style building with a cafeteria, classrooms, reading rooms, offices and dormitories which is envisioned to become a joint learning and living space for local and international students.
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Dan Martin: Expect fireworks and tricky tactics in UAE Tour finale
Irishman targeting overall classification in team's home race
Dan Martin (UAE Team Emirates) at Volta a la Comunitat Valenciana (Image credit: Getty Images)
Dan Martin (UAE Team Emirates) (Image credit: Getty Images)
Dan Martin believes that Tuesday's stage 3 summit finish on Jebel Hafeet is likely to decide the overall winner of the first UAE Tour. However, he says that the length and potential wind on the newly introduced Jebel Jais during stage 6 a few days later will make for a tactically difficult finale to the race.
Dan Martin upbeat after fifth place on Valenciana's toughest finish
UAE Tour: Gaviria wins stage 2
UAE Tour: Gaviria takes 'special victory' at team's home race
Meintjes targeting Tour de France in 2019
Martin (UAE Team Emirates) recced some of the route ahead of the race start and is one of the few riders who has seen both summit finishes – with Movistar's Alejandro Valverde another. Jebel Hafeet is half the distance of Jais – at 10 kilometres - while its gradients are much less steady, and Martin is expecting the fireworks to come on that climb.
"I've seen both climbs. Jebel Hafeet suits me and then the longer climb on stage 6 will depend on how the wind is. I think with the easier gradient, the wind could make a bigger difference and tactically it will be really tricky," Martin told Cyclingnews.
"I think Hafeet is the one that will be a lot more aggressive. If you take the jersey on Hafeet then you're probably the strongest climber and then it's just about defending on Jais on stage 6. It's a long climb, it's a different effort to Hafeet and it's long and steady. It's not super steep, but the top is hard, and nobody has done a 45-minute climb this year so it's obviously a big unknown."
Martin rode the Tour of Oman in 2016, but it is the first time that he has raced in the UAE. The heat will be an adjustment from the cooler climate of Europe, but it's not just the temperatures that Martin will have to get used to. The style of racing, with the major climbs all situated right at the end of the stages, will also be new.
"We were laughing earlier in the week that this is the only race where there are no downhills," Martin said. "It's either flat, flat or flat, uphill. It's a different kind of racing because you don't have that endurance climb after climb after climb, which suits some guys. It's flat all day and that change of rhythm at the end when you've been riding flat all day with big gears and fast speed all day, that's a different kind of racing to what we get in Europe. I've never done that kind of racing so I didn't know how I will react."
The UAE Tour is the second race of the season for Martin after the Volta a la Comunitat Valenciana, where he finished fifth overall. Riding for the home team, the week-long race has been a major priority for him heading into the 2019 season.
UAE Team Emirates lost 36 seconds to Jumbo-Visma and Primoz Roglic in the opening team time trial. It is plenty of time for Martin to try and make up over the coming days, but he still intends to make a mark on the overall classification.
"We go to every race with the same attitude, obviously this one we come here with the best team possible and in our best condition, whereas other teams it might not have been an objective. We're in good fitness and good condition, and hopefully that makes getting results easier," said Martin.
"It's a priority for the team. They asked me to be in good condition here. I got sick after Valencia, but I think I needed the rest. It was one of those winters where I felt really good, so I kept training harder and harder and I needed that break after Valencia to freshen up for here. I felt really good in the team time trial yesterday, so we look forward to tomorrow."


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DC NEWS: Arrow, Justice League – Throne of Atlantis, Flash
ARROW: THE TEAM DEALS WITH OLIVER'S DISAPPEARANCE IN THE MID SEASON PREMIERE "LEFT BEHIND";
[BEWARE OF SPOILERS]
In the aftermath of Oliver's (Stephen Amell) fight with Ras al Ghul (Matt Nable), Diggle (David Ramsey) and Arsenal (Colton Haynes) continue to protect the city in the Arrow's absence. However, after three days without hearing from Oliver, they begin to fear the worst may have happened to their friend. Felicity (Emily Bett Rickards) refuses to believe that Oliver could be dead until Merlyn (John Barrowman) pays the team a surprise visit. Thea (Willa Holland) suspects there is something more behind Oliver's disappearance and asks Merlyn for a favor. Meanwhile, Ray (Brandon Routh) tests a part of his new suit and Laurel (Katie Cassidy) takes up the mantle of the Black Canary. Glen Winter directed the episode written by Marc Guggenheim; Erik Oleson.
And here is the trailer for the mid-season premiere episode of ARROW, titled "Left Behind", airing January 21, and posted by Spoiler TV
The CW has released a description for "The Sound and The Fury," the Tuesday, Jan. 27 episode of The Flash.
Here's how the episode is described: BEWARE OF SPOILERS
"Dr. Wells' (Tom Cavanagh) former protege, Hartley Rathaway (guest star Andrew Mientus), returns to seek revenge on his mentor after being affected by the particle accelerator explosion. Now able to manipulate sound waves, the brilliant Rathaway is a dangerous threat to both Wells and The Flash (Grant Gustin).
"Meanwhile, Iris (Candice Patton) is thrilled when she's hired by the Central City Picture News as their newest cub reporter. Unfortunately, her editor (guest star Tom Butler) pairs her with aveteran reporter, Mason Bridge (guest star Roger Howarth), who wants nothing to do with her.
"Cisco (Carlos Valdes) recalls his first day on the job at S.T.A.R. Labs when he met Hartley and Caitlin (Danielle Panabaker). Joe (Jesse L. Martin) asks Eddie (Rick Cosnett) for a favor but asks him to keep it a secret from Barry."
The Flash and Green Lantern also appears in this Justice League THrone of Atlantis new clip. The animated movie will be released on Blu-Ray and DVD January 27.


Air Canada has agreed to participate in a blockchain-based travel distribution platform under development by Winding Tree. The carrier will integrate Air Canada's direct connect application programming interface with Winding Tree's public blockchain platform, "giving blockchain-savvy users the ability to access our content directly from the source," according to Air Canada director of global product distribution Keith Wallis. Air Canada is the first North American airline to work with Winding Tree, though others around the world already have announced partnerships. This month, Air France-KLM announced an agreement to test and provide feedback on the technology. Last year, Lufthansa Group and Air New Zealand also agreed to be partners.