text:
\section{Introduction}

The crossover between classical and quantum regimes in frustrated
magnets has been an important theoretical question in the last few
decades. This issue is particularly important in understanding the
nature of the quantum spin liquid phases which may arise at low
temperature due to extreme quantum fluctuations. In the classical
regime, there may exist a window of temperatures below the Curie-Weiss
scale, where the correlated spin moments are thermally fluctuating
within the degenerate manifold of classical ground states.  This is
the cooperative paramagnetic state, or the so-called classical spin
liquid.  In the quantum regime, it is clearly not possible to maintain
such a state down to zero temperature as the quantum ground state
should be unique (up to a topological degeneracy in the case of
quantum spin liquids).  An important question is how much information
about the degenerate manifold of classical ground states is encoded in
the emergent quantum spin liquid at zero and low temperatures.  Such a
question may be especially relevant for two dimensional spin liquid
phases which show no finite temperature phase transition, but only
crossovers.

One natural place to look for the clue for this question is the
dynamical spin correlation or the dynamical spin structure factor. A
recent work on the Kitaev model\cite{kitaev_anyons_2006} in two
dimensions investigates the dynamical spin correlations of the
classical Kitaev model via Landau-Lifshitz (LL)
dynamics~\cite{Samarakoon17}. The resulting dynamical structure factor
was compared with that of the quantum model\cite{knolle_dynamics_2014,
knolle_dynamics_2015, baskaran_exact_2007}, which is exactly solvable
and supports a quantum spin liquid ground state with gapless Majorana
fermion excitations.  There exist two crossover temperatures, $T_v$
and $T_Q$, in the Kitaev model on the honeycomb lattice, as seen in
the specific heat.\cite{PhysRevB.92.115122} At $T < T_v$, the vison or
flux gap is larger than the temperature scale so that the system is
essentially characterized by the zero temperature ground state. When
$T_v < T < T_Q$, the flux degree of freedom is thermally disordered,
but the Majorana fermions are still well defined. For $T > T_Q$, the
system crosses over to the classical regime. It was found that the
dynamical spin correlations in the quantum model at $T > T_v$ are
remarkably similar to those of the cooperative paramagnetic regime of
the classical model at finite temperature.  Moreover, the dynamical
structure factor of the quantum model knows about the zero mode
structure of the classically degenerate manifold even when $T _v < T <
T_Q$.  This suggests that all the classically degenerate spin states
are participating in the quantum fluctuations down to $T \sim T_v$,
which eventually lead to the emergence of the quantum spin liquid
phase at low temperature $T < T_v$.

In principle, it is not necessary that the full degenerate manifold of
the classical states is involved in the formation of the quantum spin
liquid at low temperature, since thermal entropy or zero-point quantum
fluctuations may select a subset of the full degenerate manifold at
some intermediate temperature.  On the other hand, when the full
degenerate manifold is participating in quantum fluctuations at low
temperature, as the case of the Kitaev model for $T_v < T < T_Q$, and
if the spin correlations remain short-ranged, it is highly suggestive
that the zero temperature ground state would indeed be a quantum spin
liquid.  An alternative choice for the zero temperature ground state
could be a magnetically ordered state or a quantum critical point,
which would show the development of long-range dynamical spin
fluctuations. In the case of the Kitaev model, we already know that
this is not the case, and that the zero temperature ground state is a
quantum spin liquid. One may, however, be able to use this lesson to
infer the possible presence of a quantum spin liquid in models which
are not exactly solvable.

  In the current work, we investigate the dynamical spin correlations
in the classical and quantum $\Gamma$ model\cite{rau_generic_2014}
(defined below) on the honeycomb lattice, which is known to possess
macroscopically degenerate manifold of classical ground
states\cite{rousochatzakis_classical_2017}, while the quantum model is
not exactly solvable. This model represents the bond-dependent
anisotropic and symmetric spin interactions on the honeycomb lattice:
  \begin{equation} {\cal H} = \;\; \mathrm{\Gamma }\sum_{\alpha \neq
\beta \neq \gamma }{\sum_{\left\langle {\bm r}, {\bm r}' \right\rangle
\ \in \ \gamma }{\mathrm{(}S^{\beta }_{\bm r} S^{\alpha }_{{\bm
r}'}\mathrm{+}S^{\alpha }_{\bm r} S^{\beta }_{{\bm r}'} \mathrm{)}}},
    \label{gammamodel}
  \end{equation} where $S^\alpha_{\bm r}$ are spin operators at sites
$\bm{r}$ of a honeycomb lattice, and $\alpha,\beta,\gamma=x,y,z$. Such
interactions (as well as the Kitaev interaction mentioned above) arise
in strongly spin-orbit coupled Mott insulators such as Li$_2$IrO$_3$
and $\alpha$-RuCl$_3$, where Ir$^{4+}$ or Ru$^{3+}$ ions form
effective $J=1/2$ local moments.  Currently, the relative importance
of the Kitaev and $\Gamma$ interactions is an important issue in
theoretical and experimental investigations of this class of
Kitaev-like materials\cite{jackeli_mott_2009,ybkim_2014,
rau_generic_2014, plumb_2014, sears_magnetic_2015,
johnson_monoclinic_2015, rau_spin-orbit_2016, winter_challenges_2016,
winter_models_2017, trebst_2017, sears_phase_2017,
do_incarnation_2017, hentrich_unusual_2018, wolter_field-induced_2017,
winter_breakdown_2017, winter_probing_2018}.  For instance, the
dominance of one of these interactions or the cooperation of these
two interactions may lead to possible emergence of quantum spin liquid
in these materials, especially in the presence of external pressure or
magnetic field.

We first use the Landau-Lifshitz dynamics to compute the dynamical
structure factor in the classical model at finite temperature.  It is
shown that the zero mode structure of the degenerate manifold of
classical ground states is reflected in the low frequency part of the
dynamical spin fluctuation spectra.  For example, in the case of the
antiferro-sign of the $\Gamma > 0$ interaction, the structure factor
at low frequencies is suppressed at the $\bm \Gamma$ and $\bm X$
points of the Brillouin zone, which we explain using the constraints
on the classical spin states which belong to the degenerate manifold.
Next, we employ the Martin-Siggia-Rose (MSR) formulation of Langevin dynamics
to further understand the nature of the dynamical spin correlations.
These two different methods lead to essentially the same dynamical
spin correlations, leading to the conclusion that the system itself
may be acting as an effective thermal bath. Furthermore, it is shown
that the low frequency response is relaxational and reflects the zero
mode structure, while the higher frequency response is mostly
precessional, and some characteristic precessional modes exist at
finite frequencies.  The evolution of dynamical spin correlations is
also investigated as a function of temperature
for the comparison with the quantum model.

The dynamical spin structure factor in the quantum $\Gamma$ model is
studied by exact diagonalization via the shifted Krylov subspace
method, which is combined with typical quantum state approach at
finite temperature. In previous
studies\cite{catuneanu_path_2018}, it was shown that there exist
two crossover temperatures, $T_1 \sim 0.03 \Gamma$ and $T_2 \sim 0.4
\Gamma$, in the specific heat, similar to the case of the Kitaev
model.  $T_2$ marks the crossover from the high temperature classical
regime to the quantum regime.  We find that the dynamical spin
correlations at low frequencies in the quantum model show distinct
signatures of the zero mode structure of the degenerate manifold of
classical ground states even when $T_1 < T < T_2$, which gradually
crosses over to the low temperature extreme quantum limit for $T <
T_1$. This behavior is reminiscent of the dynamical spin correlations
in the Kitaev model, where correlations as a function of temperature
are remarkably similar to the classical result.  This means that the
short-range spin fluctuations from the degenerate manifold persist
even in the quantum regime of $T_1 < T < T_2$.  On the other hand, the
dynamical spin correlations at zero temperature, while they remain
short-ranged, show features that are not present in the classical
model.  In the case of $\Gamma$ model, we currently do not know what
the quantum ground state is. One possibility is that below a certain
temperature a symmetry is broken due to order by quantum
disorder\cite{rousochatzakis_classical_2017}. Interestingly, however,
recent DMRG and exact diagonalization studies suggest possible
presence of a quantum spin liquid ground state in the $\Gamma$
model\cite{gohlke_quantum_2018}.  Since we do not have an analytical
understanding of the underlying quasiparticles in the $\Gamma$ model,
we cannot make a more precise connection to underlying quantum degrees
of freedom, which was possible in the case of the Kitaev model.
Nonetheless, the phenomenological similarity to the classical-quantum
correspondence in the Kitaev model is striking.  We may speculate that
the entire degenerate manifold of classical states would participate
in quantum fluctuations that lead to the formation of the quantum
ground state at zero temperature, such as a quantum spin liquid
phase. Our findings will help understanding this outstanding issue and
possible connection to experiments on Kitaev-like materials.

The rest of the paper is organized as follows. In section
\ref{sec:LL}, we present numerical results obtained from the LL
dynamics of the classical model. Section \ref{sec:lan} describes how
qualitatively similar results can be obtained analytically within an
MSR formalism. The dynamic correlations of the corresponding quantum
model are given in section \ref{sec:ed}. We conclude with a discussion
of our main findings in light of recent experiments in section
\ref{sec:dis}, while details of our calculations are relegated to the
appendices.

\section{Landau-Lifshitz dynamics}
\label{sec:LL}

We study the dynamical spin correlations of the $\Gamma$ model,
Eq. (\ref{gammamodel}),
whereby the spin operators are replaced by classical vectors in the
Heisenberg equation of motion. The resulting Landau-Lifshitz (LL)
equation of motion is
\begin{equation} \frac{d {\bm S}_{\bm r}}{dt}\mathrm{=}{\bm S}_{\bm r}
\mathrm{\times }{\bm B}_{\bm r},
\label{eq:LL}
\end{equation} where ${\bm B}_{\bm r}$ is the molecular field
acting on the spin ${\bm S}_{\bm r}$. This LL equation can be solved
numerically by applying a fourth order Runge-Kutta algorithm with
adaptive step size. The average over configurations at a given
temperature $T$ is obtained from the Metropolis Monte Carlo sampling
method. We note that a closed LL dynamics is more appropriate than
Langevin dynamics when the experiment is much faster than the
spin-lattice relaxation, which is the typical case in inelastic
neutron-scattering experiments. The simulations are performed on a
finite lattice of 30$\times$30 unit-cells (1800 spins) with periodic
boundary conditions.

Fig.~\ref{fig01} shows the trace of the dynamical spin structure
factor, $S\left( {\bm Q},\omega \right)=\ \sum_{\alpha }{S^{\alpha
\alpha }\left({\bm Q},\omega \right)}$, obtained for the
antiferromagnetic (AFM) (${ \mathrm \Gamma }>0$) and ferromagnetic
(FM) ($\mathrm{\Gamma }<0$) versions of the $\Gamma$-model.  As
expected for a liquid state, $S\left( {\bm Q},\omega \right)$ exhibits
a continuum of low and high-frequency modes.  The low-frequency (zero)
modes arise from the very slow dynamics through different classical
ground states. The number of zero modes is macroscopic because of the
extensive residual entropy of the ground state manifold. This dynamics
is expected to be {\it relaxational} because the average of the local
field over a period $2 \pi/\omega$ is equal to zero.
In contrast, the high-frequency modes correspond to the much faster
spin precession around the local fields produced by {\it a given
  ground state configuration}.
Accordingly, the average of the local fields ${\bm B}_{\bm r}$ over a
period $2 \pi/\omega$ remains finite.

Both, the low and high-frequency modes, contain relevant information
about the liquid state. The momentum distribution of the zero-energy
modes is a direct consequence of the set of constraints defining the
ground state manifold.  Specifically, we show in Appendix
\ref{sec:zeromodes} that the fourier transform $S^\alpha({\bf
  q})=\sum_{\bf r}S_{\bf r}^\alpha e^{i{\bf q}\cdot{\bf r}}$ of any
state $S^\alpha_{\bf r}$ in the ground state manifold, vanishes for
both ${\bf q} = \bm\Gamma$ and ${\bf q} = \bf{X}$.
As a result, the low-energy spectral weight of $S^{\alpha \alpha } (
{\bm Q},\omega)$ is suppressed at the ${\boldsymbol \Gamma}$ and ${\bm
  X}$ points of the Brillouin zone [see
Fig.~\ref{fig02}~(a)]. Correspondingly, as shown in
Fig.~\ref{fig02}~(b)-(d), the missing low-energy spectral weight at
these two points is shifted to frequencies of order $\Gamma$. In other
words, magnetic excitations with wave vectors ${\boldsymbol \Gamma}$
and ${\bm X}$ are purely precessional. Indeed, as shown in
Fig.~\ref{fig02}, the precessional modes have highest intensity at
these two wave vectors.  As we will see later, the low-energy modes of
the quantum $S=1/2$ model inherit this structure.  The high-energy
modes contain information about the magnitude and spatial distribution
of the instantaneous local fields ${\bm B}_{\bm r}$ of a typical
ground state spin configuration. The dispersion of these modes
contains information about the magnetic correlation length of the spin
liquid state.

\begin{figure}[htp]
  \centering
  \includegraphics[width=0.45\textwidth]{Figure01}
  \caption{Trace of the dynamical magnetic structure factor
    $S\left({\bm Q},\omega \right)=\ \sum_{\alpha }{S^{\alpha \alpha
      }\left({\bm Q},\omega \right)}$ for (a) AFM ($\mathrm{\Gamma
    }>0$) (b) FM ($\mathrm{\Gamma }<0$) $\Gamma$-models along the
    Brillouin Zone path, ${\bm K}-{\bm \Gamma}-{\bm M}-{\bm Y}-{\bm
      X}-{\bm K}-{\bm M}$, as depicted in the inset.}
  \label{fig01}
\end{figure}

\begin{figure}[htp]
  \centering
  \includegraphics[angle=0,clip,width=1.0\columnwidth]{Figure02}
  \caption{(a) Elastic component of the trace of the magnetic
    structure factor $S({\bm Q}, \omega=0)$. (b-d)

    $S({\bm Q},\omega )$, integrated over finite energy cuts: (b)
    $\omega /\mathrm{\Gamma } = [0.1, 0.3]$, (c) $\omega
    /\mathrm{\Gamma }$ = [0.8, 1.0] and (d)$\ \omega /\mathrm{\Gamma
    }$ = [1.8, 2.0].}
  \label{fig02}
\end{figure}

\begin{figure}[htp]
  \centering
  \includegraphics[angle=0,width=1.0\columnwidth]{Figure03}
  \caption{ $S({\bm r},\omega=0 )$ as a function of ${|{\bm
        r}|/a}$ (where $a$ is the lattice parameter) at $T= 10^{-5}
    \Gamma$.

  }
  \label{fig03}
\end{figure}

To gain more insight on the structure of the zero-energy modes,
we also present the real space spin-spin correlation function, $S({\bm
  r},\omega )$, as a function of $ \omega $ and $T$.  Fig.~\ref{fig03}
shows the elastic contribution $S({\bm r},\omega=0 )$ for different
distances up to fifth nearest neighbors (NN) and $T= 10^{-5} \Gamma$
(calculations need to be done at finite $T$ to have fluctuations and
be able to exploit the fluctuation-dissipation theorem).  Remarkably,
this is significant only for the on-site and for the
third-nearest-neighbor ($|{\bm r}|/a=2$, where $a$ is the lattice
parameter) correlation functions.  The values obtained for other
distances are smaller than the statistical error of the MC
calculation. Therefore, the fast exponential decay of the elastic
contribution indicates that the magnetic correlation length is of
order $2a$.

A similar behavior is observed in the static real space spin-spin
correlation function, $\tilde{S}^{\alpha\beta} ({\bm r})=\left\langle
  S^{\alpha }_{\bm 0 }S^{\beta }_{\bm r}\right\rangle =\
\int{S^{\alpha\beta}\left({\bm r},\omega \right)d\omega }$, shown in
Fig.~\ref{fig04}. This figure also includes off-diagonal components of
the spin-spin correlation function.  In all the cases, the correlation
function is significant only for distances $|{\bm r}|$ equal or
smaller than the separation between third nearest neighbors (opposite
sites of each hexagon).  Moreover, a subset of the nine
spin-spin correlator components $\alpha\beta$ vanishes, for any given
$\bm r$. The form of the real space correlations, as depicted in
Fig.~\ref{fig04}, is well accounted for by considering the symmetries
of the Hamiltonian, Eq. \ref{gammamodel}. To show this, we begin by
considering the three ways in which one can decompose the honeycomb
lattice into hexagon plaquettes, shown in Fig. \ref{symm}. With each
plaquette of a given decomposition we associate six spin components,
one from each site around the plaquette. Specifically, a spin
component is associated with a neighboring hexagon plaquette if it is
of the same type as the bond connecting it with a neighboring
plaquette of the same decomposition.  There exist three symmetry
operations~\cite{rousochatzakis_classical_2017}, one for each plaquette
decomposition, which correspond to $\pi$ spin rotations about an axis that depends on
the sublattice which each spin belongs to. For example, the
symmetry operation corresponding to the white plaquettes in
Fig. \ref{symm}, corresponds to a $\pi$-rotation about the $x$-axis for sublattices 1 and 4,
about the $y$-axis for sublattices 2 and 5 and about the $z$-axis for sublattices 3 and 6.
This transformation leaves the spin components $\{S_1^x, S_2^y, S_3^z, S_4^x, S_5^y,
S_6^z\}$ invariant (the subscript is the  six
sublattice index), while it changes the sign of the other ones. In appendix \ref{sec:symm}, we show that these
symmetries, which are also symmetries of the quantum model, result in
vanishing correlations between spin components which are associated
with plaquette of different decompositions, according to the rule we
just described.

 However, the spin-spin correlations are further restricted in the
classical limit. Classically, the three components of each spin
commute with each other, and as a result, one can define a local transformation that flips the sign of
an individual spin component. The classical version of the $\Gamma$ model is invariant under
a {\it local} symmetry transformation that changes the sign of
one spin component of each of the six spins in a  {\it single} hexagon plaquette.
The spin component that changes  sign is the one corresponding to the only bond which does not connect
two spins in the same hexagon~\cite{rousochatzakis_classical_2017}. For instance, the symmetry transformation changes the sign of $\{S_1^x, S_2^y, S_3^z, S_4^x, S_5^y, S_6^z\}$ for a {\it single} white hexagon plaquette.
This is the local symmetry that gives rise to the macroscopic degeneracy of the classical ground state
manifold. Consequently, the correlation function $\left\langle
S^{\alpha }_{\bm 0 }S^{\beta }_{\bm r}\right\rangle$ vanishes unless
both $S_0^\alpha$ and $S_{\bm r}^\beta$ belong to the same
single hexagon. This restricts correlations to third neighbor at most,
and determines the specific components which have non zero
correlations, as seen in Fig. \ref{fig04}. For example, only the
diagonal components of the on-site correlations are non-zero, since
different components of a given spin are associated with different
plaquettes, and thus, uncorrelated.  Similarly, the only other
non-vanishing diagonal components of the spin-spin correlation
function appears for third neighbors, e.g., for the white plaquette
mentioned earlier we have only a finite $\left\langle S_1^xS_4^x
\right\rangle$ in addition to the on-site correlation. Similar
considerations restrict finite off-diagonal correlations to nearest and
second nearest neighbors around one plaquette.

\begin{figure*}[htp]
  \centering
  \includegraphics[trim={0cm 0cm 0cm 0cm},clip,width=1.0\textwidth]{Figure04}

  \caption{Static spin-spin correlation function,
    $\tilde{S}^{\alpha\beta}=\left\langle S^{\alpha }_{\bm o }S^{\beta
      }_{\bm r}\right\rangle =\ \int{S^{\alpha\beta}\left({\bm r},\omega
      \right)d\omega }$ mapped on the real-space lattice with respect to
    an arbitrary origin denoted by the cross ($\times $).  The
    temperature of the simulation is $T= 10^{-5} \Gamma$.}
  \label{fig04}
\end{figure*}

\begin{figure}[t]
  \includegraphics[clip,width=1.0\columnwidth]{Sym}
  \caption{Six sublattice decomposition of the honeycomb lattice. We
    also show the three different decompositions of the lattice into
    isolated hexagonal plaquettes.}
  \label{symm}
\end{figure}

 Fig.~\ref{fig05} shows the temperature and frequency
dependence of $S\left({\bm r} ,\omega \right)$ for several values of
${\bm r}$.  In agreement with the symmetry analysis given in Appendix~\ref{sec:symm},
$S\left({\bm r} ,\omega \right)$ vanishes for any frequency when ${\bm r}$ connects second
nearest neighbor sites [see Figure~\ref{fig05}~(b)]. The temperature dependence of $S\left({\bm r} ,\omega \right)$
for other values of ${\bm r}$ indicates a crossover from partially
precessional to fully diffusive behavior at a temperature of order
$\Gamma$.  The temperature dependence of $S\left( {\bm Q} ={\bm \Gamma
  },\omega \right)$ shown in Figure~\ref{fig06} confirms this
crossover, indicating that the system evolves continuously from a
low-temperature ($T< \Gamma$) correlated liquid (classical $\Gamma$
liquid) to a high-temperature paramagnetic state.

\begin{figure}[htp]
  \centering
  \includegraphics[trim={0cm 0cm 0cm 0cm},clip,width=1.0\columnwidth]{Figure05}
  \caption{$S\left({\bm r},\omega \right)$ as a function of
    temperature and energy ($\hbar \omega $)for AFM ($\Gamma>0$) Gamma
    model.  Panels (a), (d) and (e) show $-S\left({\bm r},\omega
    \right)$ for ${\bm r}$ connecting 1st, 3rd and 5th
    nearest-neighbor sites, respectively. Panel (b) shows $S\left({\bm
        r},\omega \right)$ for ${\bm r}$ connecting nearest-neighbor
    sites. Panel (c) shows that $S\left({\bm r},\omega \right)=0$ for
    ${\bm r}$ connecting second nearest neighbor sites.}
  \label{fig05}
\end{figure}

\begin{figure}[htp]
  \centering
  \includegraphics[clip,width=\columnwidth]{Figure06}
  \caption{Temperature evolution of $S ({\bm Q} ={\bm \Gamma
    },\omega)$ for AFM ($\Gamma>0$) Gamma model. }
  \label{fig06}
\end{figure}

\section{Langevin dynamics}
\label{sec:lan}

Although, as noted in the previous section, neutron scattering
experiments are faster than spin-lattice relaxation, a Langevin
approach may still be used to analytically understand dynamic
correlations in LL dynamics. The non-linear nature of
Eq. (\ref{eq:LL}) gives rise to strong relaxation due to inelastic
processes, in addition to the more direct precessional dynamics. In
other words, the fluctuating spins act as their own heat bath --
leading to strong relaxation. At a phenomenological level, it is
possible to capture the two types of spin dynamics in a generalized
Langevin equation, where a linear term describes the spin relaxation,
while precession is included in a residual non-linear term.  We thus
propose to study the stochastic dynamics of a system of soft classical
spins~\cite{Colon09} $S_i^\alpha$, given by
\begin{equation}
  \label{eq:lan}
  \frac{\partial S_i^\alpha}{\partial t} = g\epsilon_{\alpha\beta\gamma}S_i^\beta
  \frac{\partial H}{\partial S_i^\gamma} - \gamma\frac{\partial{H}}
  {\partial S_i^\alpha} + \eta_i^\alpha,
\end{equation}
where $i,j$ denote a site on a honeycomb lattice, $\alpha,\beta=x,y,z$ and
the noise term $\eta_i^\alpha$ obeys
\begin{equation}
  \label{eq:noise}
  \left\langle\eta_i^\alpha(t)\eta_j^\beta(t')\right\rangle
  = 2\gamma T \delta_{ij}\delta_{\alpha\beta}\delta(t-t').
\end{equation}
As described below, the unitless phenomenological parameters --
$\gamma$ setting the relaxation rate and $g$ the precession rate --
are chosen by comparing the dynamical correlations with the results of
the LL simulation, while $T$ is simply the temperature.  The spins are
taken to be soft with mass $\Delta$, and with a general nearest
neighbor spin interaction, $K_{ij}^{\alpha\beta}$, as given by the
following Hamiltonian
\begin{equation}
  \label{eq:H}
  H = \sum_{\alpha\beta}\sum_{\braket{ij}}K_{ij}^{\alpha\beta}
  S_i^\alpha S_j^\beta + \frac{\Delta}{2}\sum_{i\alpha}\left(S_i^\alpha\right)^2,
\end{equation}
The mass $\Delta$ is an additional, temperature dependent,
phenomenological parameter which determines the average spin size
$\braket{S_i^2}$.  Quadratic Hamiltonians of this type are suitable
for studying spin dynamics in cases where there is no long range
order. We will apply this to the classical $\Gamma$ model, which has
macroscopic degeneracy in its ground state, preventing long range
order even at low temperatures. A similar treatment for the Kitaev
model is given in the Appendix. Following a path integral formulation
of the MSR approach\cite{martin_statistical_1973,
  de_dominicis_field-theory_1978, wachtel_transverse_2014}, we write a
generating functional for dynamical correlations as
\begin{equation}
  \label{eq:Z1}
  Z\!=\!\left\langle\!\int DS\,|M|\,
    \delta\!\left(\frac{\partial S_i^\alpha}{\partial t}\!-\!
      g\epsilon_{\alpha\beta\gamma}S_i^\beta \frac{\partial H}{\partial S_i^\gamma}
      \!+\!\gamma\frac{\partial{H}} {\partial S_j^\alpha}
     \!-\! \eta_i^\alpha\right)\!\right\rangle_\eta \!,
\end{equation}
where $\braket{\cdots}_\eta$ denotes averaging over the noise
fluctuations $\eta$, and $M$ is a Jacobian matrix. For the model we
consider here we may take the determinant $|M|=1$. Writing the delta
function as an integral over $\hat S_i^\alpha$, and averaging over
$\eta$, we obtain
$Z = \int D\hat S\,DS\,e^{-\mathcal{S}}$ where the MSR action is given
by
\begin{eqnarray}
  \label{eq:S1}
  \mathcal{S} & = & -\int dt\left[\hat S_i^\alpha\left(\partial_tS_i^\alpha
      +\gamma K_{ij}^{\alpha\beta}    S_j^\beta+\gamma\Delta S_i^\alpha\right)
    \right. \nonumber \\ & & \left.\qquad\qquad +\gamma T (\hat S_i^\alpha)^2
    -g\epsilon_{\alpha\beta\gamma}\hat S_i^\alpha S_i^\beta K_{ij}^{\gamma\delta}
    S_j^\delta\right],
\end{eqnarray}
Within this formalism it is possible to calculate dynamical
correlation functions, using perturbation theory in $g$.

\begin{figure}[bb]
  \centering
  \includegraphics[width=\linewidth]{diagrams}
  \caption{Feynman diagrams for the MSR formalism: (a) Bare response
    function. (b) Bare correlation function. (c) Precession
    vertex.  (d) Self-energy diagram. (e) Perturbative
      expansion of the dressed correlation function, in powers of the
      self-energy $\Sigma$, see Eq. (\ref{eq:C}).}
  \label{fig:diagrams}
\end{figure}
\emph{Zeroth order in} $g$: When $g=0$, the dynamics is purely
relaxational. The bare response Green's function, defined as
\begin{equation}
  \label{eq:G0}
  \left(G_0(\omega)\right)_{ij}^{\alpha\beta}\equiv\left\langle \hat
    S_i^\alpha(-\omega)S_j^\beta(\omega)    \right\rangle_0,
\end{equation}
is given by (its inverse)
\begin{equation}
  \label{eq:G0inv}
  \left(G^{-1}_0(\omega)\right)_{ij}^{\alpha\beta} = (-i\omega+\gamma\Delta)
  \delta_{\alpha\beta}\delta_{ij}  + K_{ij}^{\alpha\beta}
\end{equation}
We will represent this diagrammatically using Fig. \ref{fig:diagrams}a.
Similarly, the bare correlation function is given by
\begin{equation}
  \label{eq:C0}
  \left(C_0(\omega)\right)_{ij}^{\alpha\beta} \equiv \left\langle
    S_i^\alpha(-\omega)S_j^\beta(\omega)\right\rangle_0 = 2\gamma T \left(
    G_0^\dagger(\omega)G_0(\omega)\right)_{ij}^{\alpha\beta}
\end{equation}
Diagrammatically, this is represented in Fig. \ref{fig:diagrams}b
where the noise vertex is represented by a dot, $\bullet = 2\gamma T$.

In the pure $\Gamma$ model, which is defined by
\begin{equation}
  \label{eq:Kitaev}
  K_{ij}^{\alpha\beta}=\left\{
    \begin{array}{cc}
      \Gamma & \alpha\ne\beta\ne\braket{ij} \\ 0 & {\rm otherwise}
    \end{array}\right. ,
\end{equation}
the classical degrees of freedom can be divided into sectors -- one
for each hexagon. For example, as discussed in the previous section,
going around one of the white hexagons in fig. \ref{symm}, we can
identify six spin components which interact only within
themselves. Their dynamics is independent of the rest of the system,
manifesting the macroscopic degeneracy of the classical system. We
rename these degrees of freedom as follows,
\begin{equation}
  \label{eq:sigmas}
  \left\{ S_1^x, S_2^y, S_3^z, S_4^x, S_5^y, S_6^z\right\} \equiv \left\{\sigma_1, \sigma_2,
    \sigma_3, \sigma_4, \sigma_5, \sigma_6\right\}.
\end{equation}
The Hamiltonian, restricted to this sector, is given by
\begin{equation}
  \label{eq:Hsigma}
  H_{\rm hexagaon} = \sum_{l=1}^6 \left(\Gamma \sigma_l\sigma_{l+1} + \frac{\Delta}{2}
    \sigma_l^2\right).
\end{equation}
The energy eigenvalues, which determine the relaxation rate, are
$\varepsilon_m = 2\Gamma\cos{\pi m}/{3}+\Delta,\quad m=1\dots 6$.
Clearly, the model is stable only for $\Delta>2|\Gamma|$.  The $g=0$
dynamical correlation function within these six spin components is
given by
\begin{equation}
  \label{eq:hexcor}
  \left\langle \sigma_l(\omega)\sigma_{l'}(\omega')\right\rangle
  \!=\! \frac{1}{6}\!\sum_{m=1}^6\!\cos\!\left(\!\frac{\pi m(l-l')}{3}\!\right)
  \frac{2\gamma T\,2\pi\delta(\omega+\omega')}
  {\omega^2 + \gamma^2\varepsilon_m^2},
\end{equation}
while the correlation with spin components which do not appear in
Eq. (\ref{eq:sigmas}) is identically zero.  $\Delta$ may be chosen so
that $\braket{\sigma_l^2}$ is a constant; at the $g=0$ level $\Delta$
should obey $\braket{\sigma_l^2}=\sum_m(T/6\varepsilon_m)=1$. Clearly,
the dynamics for $g=0$ is purely relaxational, with a peak at
$\omega=0$. Thus, $\gamma$ can be chosen such that
  Eq. (\ref{eq:hexcor}) reproduces the width of the low energy peak as
  obtained in the LL simulations. Focusing on the dynamic structure
factor $\braket{S^\alpha({\bf q},\omega)S^\alpha(-{\bf q},-\omega)}$,
we note that for each hexagon $\braket{S^x_lS^x_{l'}}\ne 0 $ only for
$l,l'=1,4$, $\braket{S^y_lS^y_{l'}}\ne 0$ only for $l,l'=2,5$ and
$\braket{S^z_lS^z_{l'}}\ne 0$ only for $l,l'=3,6$, in line with the
symmetry consideration of the previous section and in Appendix
\ref{sec:symm}. In the anti-ferromagnetic $\Gamma$ model, the lowest
eigenvalues is $\varepsilon_3=-2\Gamma+\Delta$. Noting that there are
non-zero correlations only for $l-l'=0,3$, we find that the
contribution of this eigenvalue to the spectrum at $\bm{\Gamma}$
vanishes, and one would expect only the higher energy modes,
i.e. faster relaxations, to contribute at this momentum. A similar
argument holds for the low energy correlations at $\bm{X}$. Thus we
find a depletion in the dynamic structure factor at $\bm{\Gamma}$ and
$\bm{X}$, echoing the analysis of the zero modes in the previous
section.

\begin{figure}[tt]
  \centering
  \includegraphics[width=\linewidth]{msr_gamma}
  \caption{Dynamic structure factor as obtained from Eq. (\ref{eq:C}),
    for (a) the AFM $\Gamma>0$, and (b) the FM $\Gamma<0$ models. Here
    we have used $\gamma=0.12$, $\Delta=2.05\Gamma$ and
    $g^2T=0.04\Gamma$.}
  \label{fig:msr_gamma}
\end{figure}
\emph{Perturbation theory in $g$.} It is possible to treat the
precession term using diagrammatic perturbation theory. We represent
the \emph{symmetrized} precession vertex by Fig. \ref{fig:diagrams}c.
The dressed correlation function, $C_{ij}^{\alpha\beta}(\omega)$, can
be calculated approximately, by summing over a subset of infinite
diagrams, as shown in Fig. \ref{fig:diagrams}. Specifically, we
approximate $C(\omega)$ by a product of two infinite series,
\begin{eqnarray}
  \label{eq:C}
  C(\omega)\approx2\gamma T\left|G_0(\omega)\sum_{n=0}^\infty
    \left(\Sigma(\omega)G_0(\omega)\right)^n\right|^2,
\end{eqnarray}
where the `self energy' $\Sigma$ is calculated to leading order in
$g$.  The self energy term for the $\Gamma$ model dynamics mixes
different sectors, and therefore its calculation must be done in
Fourier space. However, the procedure is no different than in quantum
field theory, once the appropriate Feynman rules are
determined. Fig. \ref{fig:msr_gamma} shows the resulting dynamic
structure factor. Eq. (\ref{eq:hexcor}), obtained for $g=0$,
qualitatively accounts for the low frequency features, including the
depletion at $\bm{\Gamma}$ and $\bm{X}$ in the AFM case. The main
qualitative effect of finite $g>0$ on the dynamic structure factor, is
the addition of correlations peaked at finite frequency, due to the
precession of the spins. In Appendix \ref{sec:msrkitaev} we describe
the calculation for the Kitaev model, which is simpler, and can be
done in real space.  Furthermore, the closed form result for the
Kitaev model shows that the self energy is larger for the mode which
is suppressed at low energies. Similar behavior is observed in
Fig. \ref{fig:msr_gamma} for the $\Gamma$ model, where the precession
features appear at finite frequency at the same momentum positions
with depleted low energy correlations. Besides the qualitative effect
of precessional dynamics, a finite $g$ is also expected to renormalize
the values of $\gamma$ and $\Delta$ required to fit the numerical data
obtained at a given temperature.

\section{Dynamics of the spin-$\frac{1}{2}$ model}
\label{sec:ed}

\begin{figure}[tth]
\centering
\includegraphics[width=4.0cm]{Figure10}
\caption{(color online):
Finite-size honeycomb clusters with 24 spins and periodic boundary conditions.
Bonds along the three different directions are labeled as
the $x$, $y$, and $z$ bond, which are along -60$^{\circ}$, 60$^{\circ}$,
and horizontal directions, respectively.
}
\label{fig_honeycomb_18_24}
\end{figure}

\begin{figure}[hbt]
\centering
\includegraphics[width=0.5\textwidth]{fig_Gamma24_C}
\caption{(color online):
Specific heat $C/N$
of the AFM $\Gamma$ model on the $N=24$ site cluster~\cite{catuneanu_path_2018},
calculated by the typical pure quantum states approach~\cite{PhysRevE.62.4365,PhysRevLett.111.010401}.
There are two maxima in the temperature dependence of $C/N$.
The error bars
are the standard errors estimated by 32 random initial vectors.
}
\label{FigC_S1half}
\end{figure}

\begin{figure*}[hbt]
\centering
\includegraphics[width=1.05\textwidth]{fig_Gamma}
\caption{(color online):
Equi-energy slices of the dynamical spin structure factors of the $\Gamma>0$ model.
The momentum dependence of the equi-energy slices is shown by changing temperature and frequency.
From the top row to the bottom row, the equi-energy slices of the dynamical spin structure factors
are shown at $T/\Gamma=1$, $0.5$, $0.2$, and $0.1$.
The equi-energy slices are prepared by averaging the spectra within an energy window whose width is 0.1.
For visibility, the dynamical spin structure factors at discrete momenta obtained by the simulation
are interpolated. Here, the broadening factor $\eta/\Gamma =0.02$ is used (see Appendix \ref{details_of_ED} for the definition of $\eta$).
}
\label{FigSQomegaBZ}
\end{figure*}

\begin{figure}[hbt]
\centering
\includegraphics[width=0.4\textwidth]{Figure13}
\caption{(color online): Temperature evolution of
  $S(\mbox{\boldmath$Q$}=\Gamma,\omega)$ and
  $S(\mbox{\boldmath$Q$}=M,\omega)$ for the $\Gamma>0$ model.  }
\label{FigGammaM}
\end{figure}

\begin{figure}[hbt]
\centering
\includegraphics[width=0.4\textwidth]{Figure14}
\caption{(color online):
Dynamical spin structure factors of the $S=1/2$ AFM $\Gamma$ model at
(a) $T=0.5$, (b) $T=0.2$, (c) $T=0.1$, and (d) $T=0$,
along symmetry lines.
For visibility, the broadening factor $\eta/\Gamma =0.02$ is used (see Appendix \ref{details_of_ED} for the definition of $\eta$).
}
\label{Figdiagram}
\end{figure}

\begin{figure*}[hbt]
\centering
\includegraphics[width=0.6\textwidth]{Figure15}
\caption{(color online):
Real-space static spin-spin correlation function, $\langle {S}^{\alpha}_{\mbox{\boldmath$0$}} {S}^{\beta}_{\mbox{\boldmath$r$}}\rangle$ $(\alpha,\beta = x,y,z)$,
of the $S=1/2$ $\Gamma>0$ model on the 24 site cluster
with periodic boundary condition, at $T=0$.
The location of the origin $\mbox{\boldmath$0$}$ is denoted by the open circle ($\circ$).
The radiuses of the closed circles at $\mbox{\boldmath$r$}$ represent the amplitude of $|\langle {S}^{\alpha}_{\mbox{\boldmath$0$}} {S}^{\beta}_{\mbox{\boldmath$r$}}\rangle|$,
while the color of the closed circles shows $\langle {S}^{\alpha}_{\mbox{\boldmath$0$}} {S}^{\beta}_{\mbox{\boldmath$r$}}\rangle$.
Within numerical accuracy, there is no spin-spin correlation represented by a circle with a radius smaller than the width of the solid lines representing the bonds.
}
\label{FigS0SR_S1half}
\end{figure*}

\begin{figure}[hbt]
\centering
\includegraphics[width=0.5\textwidth]{fig_Gamma24_SS}
\caption{(color online):
Temperature dependence of static spin-spin correlations of the AFM $\Gamma$ model on the 24 site cluster.
Here, the error bars, which are smaller than or comparable to the symbol size,
are the standard errors estimated by several random initial vectors.
}
\label{FigfTSS_S1half}
\end{figure}

Using the exact-diagonalization method, described in Ref.~\onlinecite{yamaji2018numerical} and Appendix \ref{details_of_ED}, we study
the finite-temperature dynamical spin structure factors
of the $S=1/2$ AFM $\Gamma$ model.
Here, we use a 24 site cluster with periodic boundary conditions,
illustrated in Fig. \ref{fig_honeycomb_18_24}.  As explained below,
the dynamical spin structure factor of the quantum model shows a
gradual classical-to-quantum crossover when the temperature is
decreased.

Before going into details of the
quantum spin dynamics of the $\Gamma$ model,
we summarize the energy scale of the quantum $S=1/2$
$\Gamma$ model.
As shown in Ref.~\onlinecite{catuneanu_path_2018} and Fig.~\ref{FigC_S1half}, there
are two temperature scales given by the peaks in the temperature
dependence of the specific heat.  The higher-temperature peak appears
around $T_2/\Gamma \sim 0.4$ and the lower-temperature peak emerges below
$T_1/\Gamma \lesssim 0.03$.
The two peak structure in the temperature
dependence of the specific heat has been found in the Kitaev
model~\cite{PhysRevB.92.115122} and in the proximity of the Kitaev's
spin liquid~\cite{PhysRevB.93.174425}, although the balance of the
entropy released by these two peaks is different from that of the
$\Gamma$ model.

In Fig.~\ref{FigSQomegaBZ}, the momentum dependence of the equi-energy
slices of $S(\mbox{\boldmath$Q$},\omega)$ are shown by changing
temperature and frequency.
The equi-energy slices are prepared by
averaging the spectra within an energy window whose width is 0.1.
The momentum dependence is numerically interpolated for visibility without
changing the simulation results at the discrete momenta
$\mbox{\boldmath$Q$}$ compatible with the finite size cluster.
At $T/\Gamma = 1 > T_2/\Gamma \sim 0.4$, almost momentum-independent
behaviors of $S(\mbox{\boldmath$Q$},\omega)$ are found except around $\Gamma$ point,
where spectral weight is suppressed for $\omega/\Gamma < 1$ and is shifted to the high energy region $\omega/\Gamma > 1$.
Below $T/\Gamma = 0.5 \sim T_2/\Gamma$, the suppression of the low-energy spectral weight (or relaxational dynamics) at $\Gamma$ and $X$ points
becomes notable, which is consistent with the classical dynamics.

To examine the temperature dependence of the low energy spectral
weight, we show the temperature evolution of
$S(\mbox{\boldmath$Q$}=\bm\Gamma,\omega)$ in comparison with
$S(\mbox{\boldmath$Q$}=\bm M,\omega)$ in Fig.\ref{FigGammaM}.  Below
the high temperature scale $T/\Gamma\sim 0.4$,
$S(\mbox{\boldmath$Q$}=\bm \Gamma,\omega)$ shows reduced spectral
weight in the low energy region below $\omega/\Gamma \sim 0.5$, while
$S(\mbox{\boldmath$Q$}=\bm M,\omega)$ shows substantial spectral
weight in the low energy region. We further note that the Fourier
transformation of $S(\mbox{\boldmath$Q$},\omega)$,
$S(\mbox{\boldmath$r$}_{\ell m},\omega)$, also satisfies the symmetry
properties at finite temperatures, as discussed in section
\ref{sec:LL}.

For closer comparison with the classical dynamics, we show
$S(\mbox{\boldmath$Q$},\omega)$ at $T/\Gamma=0.5$, $0.2$, $0.1$, and $0$ along symmetry lines
in Fig.\ref{Figdiagram}.
In addition to the suppression of the low-energy spectral weight at $\Gamma$ and $X$ points,
which is in common with the classical spin dynamics,
the low-energy spectral weight for $\omega/\Gamma \lesssim 0.5$ decreases at $K$ and $Y$ upon cooling.
This suppression at the $K$ and $Y$ points is characteristic of the $S=1/2$ $\Gamma$ model.

To gain insight into the difference between the
  quantum and classical dynamics at the $K$ and $Y$ points, we examine
  the static spin-spin correlation function at zero temperature.  In
  Fig.\ref{FigS0SR_S1half}, $\langle
  {S}^{\alpha}_{\mbox{\boldmath$0$}}
  {S}^{\beta}_{\mbox{\boldmath$r$}}\rangle$ $(\alpha,\beta =
  x,y,z)$ are shown in the 24 site cluster with the periodic boundary
  condition.  These correlators in the quantum model are very similar
  to the static correlation functions of the classical model, as shown
  in Fig.~\ref{fig04}.  Due to the symmetry of the $\Gamma$ model, the
  static spin-spin correlation functions are zero for many spin pairs.
  However, there are differences among them: For example, there exist
  finite nearest-neighbor correlations $\langle
  {S}^{\alpha}_{\mbox{\boldmath$0$}}
  {S}^{\beta}_{\mbox{\boldmath$r$}}\rangle $ $(\alpha,\beta =
  x,y,z)$ for $\alpha = \beta$ and the additional second
  nearest-neighbor correlations for $\alpha \neq \beta$. The fact that
  these correlations are finite, while they are absent in the
  classical limit, indicates that quantum fluctuations are important
  even when $T>T_1$.

The most significant difference is the nearest-neighbor correlations for $\alpha=\beta$, which are  zero
in the classical model  due to the  the local symmetry discussed in Sec.~\ref{sec:LL}.
The nearest-neighbor ferromagnetic correlations in the real space
hinder the antiferromagnetic low-energy fluctuations at the $Y$ and $K$ points in the momentum space.
As a result, these correlations harden the spin fluctuations at these momenta.
In other words, these correlations suppress the relaxational dynamics and introduce the quasi-collective precessional dynamics
at these momenta.

A quantitative description of the classical-quantum crossover is
obtained by examining temperature dependence of the typical static
spin-spin correlation functions shown in Fig.~\ref{FigfTSS_S1half}.
While the off-diagonal nearest-neighbor correlations $\langle
{S}^{\alpha}_{\mbox{\boldmath$0$}}
{S}^{\beta}_{\mbox{\boldmath$r$}}\rangle$ on the $\gamma$ bond,
where $(\alpha,\beta,\gamma)$ is a permutation of $(x,y,z)$, are
dominant at temperatures above and around $T_2/\Gamma \sim 0.4$, the
diagonal nearest-neighbor correlations $\langle
{S}^{\alpha}_{\mbox{\boldmath$0$}}
{S}^{\alpha}_{\mbox{\boldmath$r$}}\rangle$ start to saturate upon
cooling for $T<T_2$.  Therefore, the classical precessional dynamics
due to the off-diagonal nearest-neighbor correlations governs the
dynamics for $T\gtrsim T_2$.  On the other hand, the emergent quantum
dynamics is generated by the diagonal nearest-neighbor correlations
for $T<T_2$.  Here, we note that dominance of the off-diagonal
nearest-neighbor correlations originates from their Curie-like
temperature dependence in the high temperature region, which is
evident in the inset of Fig.~\ref{FigfTSS_S1half}, while temperature
dependence of the diagonal nearest-neighbor and third nearest-neighbor
correlations shows $T^{-2}$ and $T^{-3}$ scaling, respectively. In
Appendix \ref{sec:highT} we show how these power-law behaviors can be
obtained using a high temperature expansion.

\section{Discussion}
\label{sec:dis}

In this work, we investigated classical and quantum dynamics of the
$\Gamma$ model, the bond-dependent symmetric and anisotropic spin
interaction on the honeycomb lattice.  Such exchange interaction
arises in strongly spin-orbit-coupled Mott insulators, in addition to
the usual Heisenberg and Kitaev (the bond-dependent Ising)
interactions\cite{rau_generic_2014, rau_spin-orbit_2016}.  There exist
a number of so-called ``Kitaev materials'' such as $\alpha, \beta,
\gamma$-Li$_2$IrO$_3$ and $\alpha$-RuCl$_3$, where the Kitaev
interaction, if dominant, may lead to a quantum spin liquid phase.
However, the strength of the $\Gamma$ interaction can be as large as
that of the Kitaev interaction, especially in the case of
$\alpha$-RuCl$_3$, according to recent ab initio
computations\cite{winter_challenges_2016}.  The presence of other
interactions has been regarded as an obstacle for realizing the
quantum spin liquid ground state in this class of materials.

On the other hand, the $\Gamma$ interaction is also highly frustrated
at the classical level, just like the Kitaev model. Given that the
strength of this interaction is significant in some materials, the
nature of the quantum ground state of the $\Gamma$ model is highly
relevant for the interpretation of the experiments. In the case of
$\alpha$-RuCl$_3$, for example, it has been speculated that the
scattering continuum seen in recent neutron scattering experiment may
come from a nearby quantum spin liquid even though the actual ground
state is a magnetically ordered state~\cite{Banerjee16,
  Banerjee17}. The magnetic order can be suppressed by external
in-plane magnetic field and the resulting paramagnetic state is
speculated to be a field-induced quantum spin
liquid\cite{sears_phase_2017,hentrich_unusual_2018,
  wolter_field-induced_2017}.  Currently it is highly debated whether
the Kitaev interaction or other interactions or both could be
responsible for the formation of a putative quantum spin liquid ground
state.

In the present work, we focused on the $\Gamma$ interaction and
pointed out the similarity to the Kitaev model, in the correspondence
between classical and quantum dynamics. We showed that the zero mode
structure of the highly degenerate manifold of the classical ground
states is reflected in the classical dynamical spin structure factor.
In addition, we clarified different roles of relaxational and
precessional dynamics in the dynamical spin structure factor of the
classical model.  Remarkably this feature survives in the quantum
model down to very low energy scales. This would imply that the full
degenerate manifold of the classical states are participating in
quantum fluctuations down to very low energy scales.  This situation
resembles the results of the Kitaev model, obtained in a previous
study~\cite{Samarakoon17}, where the quantum dynamical spin structure
factor is qualitatively similar to the classical results down to low
energies above the small flux gap in the underlying spin liquid ground
state. This correspondence in the Kitaev model was apparent even in
the temperature/energy window where the underlying low energy degrees
of freedom are Majorana fermions, not the semiclassical spins.  Since
the quantum $\Gamma$ model is not exactly solvable, we do not know the
true quantum ground state at zero temperature.  It has been suggested
that order by quantum disorder leads to a symmetry-broken
state\cite{rousochatzakis_classical_2017}. The resemblance to the
Kitaev model, however, suggests that the quantum ground state of the
$\Gamma$ model may also be a quantum spin liquid, which results from
the ``collapse'' of the degenerate classical manifold.  Such
conclusion may also be consistent with a recent DMRG computation of
the same model\cite{gohlke_quantum_2018}, where the ground seems to be
a highly correlated quantum paramagnet.  If the $\Gamma$ model can
indeed support a quantum spin liquid ground state, the presence of
this interaction in real materials may not necessarily be an
obstruction for the realization of the quantum spin liquid ground
state. The firm answer to this question would require further studies
of the quantum and classical models with both the Kitaev and $\Gamma$
interactions.

\acknowledgments

Work at ORNL is supported by the U.S. Department of Energy (DOE),
Office of Science, Basic Energy Sciences, Scientific User Facilities
Division. CDB acknowledges support from the Los Alamos National
Laboratory LDRD program. GW and YBK are supported by the NSERC of
Canada and the Center for Quantum Materials at the University of
Toronto. GW was additionally supported by the Israel Science
Foundation (Grant No. 585/13). YY was supported by JSPS KAKENHI (Grant
No. 16H06345) and was supported by PRESTO, JST (JPMJPR15NF).  This
research was supported by MEXT as ``Priority Issue on Post-K computer"
(Creation of New Functional Devices and High-Performance Materials to
Support Next-Generation Industries) and ``Exploratory Challenge on
Post-K computer" (Frontiers of Basic Science: Challengin the Limits).
Our numerical calculation was partly carried out at the Supercomputer
Center, Institute for Solid State Physics, University of Tokyo.  The
exact diagonalization (ED) calculations are partly double-checked by
using an open-source ED program package
$\mathcal{H}\Phi$~\cite{HPhi,Kawamura2017180}.

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text:
Автоматический станковый гранатомёт
Автоматический ручной гранатомёт Барышева

См. также
:Категория:Автоматические ручные гранатомёты
XM-25 — перспективный гранатомётный комплекс.

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YAY! Happy bday Mich! 2018=rave reviews and a big box office hit this summer and hopefully more!
Time really flies. It's kind of depressing, Lol.
Nice little birthday write-up from People. But once again, Where is Kyra? is not mentioned at all. What the hell?
That's nice. Maybe Michelle found time to film a secret cameo in BLL2 as Reese's mum.
My (probably typo-filled) birthday tribute to Michelle!!
HAPPY BIRTHDAY MICHELLE MY BELLE!
This photo by her stylist was liked by Elle Fanning, Josh Brolin, Ashley Judd, Cristina Ricci amongst others.


The United States Junior Chamber and the American Cancer Society: committed to the fight against cancer! The American Cancer Society is the nationwide, community-based, voluntary health organization dedicated to eliminating cancer and diminishing suffering from cancer through research, education, advocacy, and service. Since 2008, The United States Junior Chamber has formally partnered with the American Cancer Society through participation in Relay For Life events across the country. The Jaycee commitment to the American Cancer Society has resulted in an expanded partnership to defeat cancer.
Click on Find a Relay, and search by zip code or City and State to find the RFL that your team wishes to participate in.
Please make a print screen of your registration confirmation, for future reference if needed.
You are now registered to FIGHT BACK with ACS and the US Jaycees. Your team will be viewable through your local RFL event website and on the US Jaycees/RFL Non Corporate Team Page. The best part--no additional reporting is required for US Jaycees, all online donations are tracked automatically through the website. Offline donations are also reported to your USJC RFL Program Manager on a regular basis. Of course teams are encouraged to verify their information from time to time and report any discrepancies or ask any questions...anytime.
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text:
156 affordable homes included in planned housing development in Ripon - here's how to register interest
CBI: manufacturing stalls in September, outlook weak
BRITISH manufacturing output failed to expand in the three months to September for the first time since early 2013, adding to signs of a slowing in the country's economy, an industry survey showed.
Tuesday, 22nd September 2015, 2:10 pm
The Confederation of British Industry said total orders and export orders deteriorated with demand from abroad falling back to its lowest level in six months.
The monthly total order book balance from the CBI's industrial trends survey slipped to -7 in September from -1 in August. Economists had expected an unchanged reading.
Expectations for output over the next three months were the weakest since October 2013.
Rain Newton-Smith, CBI director of economics, said: "Exports are the missing link in the UK recovery at the moment, with the strong pound squeezing manufacturers' margins, even though lower commodity prices are helping to ease cost pressures.
"Meanwhile manufacturers will have an eye on China's slowdown and its effect on neighbouring markets. Boosting our export performance, alongside innovation, are vital to improving productivity.
"That's why businesses want the Government to protect export and innovation spending, alongside other growth-boosting areas, in the Comprehensive Spending Review."
Howard Archer, chief UK and European economist at IHS Global Insight, said the CBI survey will likely reinforce concerns that the economy is going through a soft patch in the third quarter, although he added that the manufacturing sector has largely been struggling throughout 2015.
Other survey evidence highlights the weakness of export orders, with manufacturers' organisation the EEF reporting in its September quarterly survey that export orders for manufacturers had dipped to a six-year low.
In addition, the manufacturing purchasing managers reported foreign orders contracted modestly in August for a fifth month running, said Mr Archer.
He added: "Weakened manufacturing activity is worrying for hopes that UK growth can become more balanced and less dependent on the services sector and consumer spending."
Across the UK, the CBI speaks on behalf of 190,000 businesses of all sizes and sectors which together employ nearly seven million people, about one third of the private sector-employed workforce.

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Search results for "Germany, Canada"
Wayward Canadian, Matthew, crushed by the isolation of being new to Berlin, turns his sexual desires toward Matthias that spiral into a dark fixation of assumed identity. Soon, this obsessive…
Country: Germany, Canada
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text:
Q: What's the purpose of Winforms controls tags? I see a 'Tag' property in the design view for most WinForms controls. I have never used this tag and want to know why I would want to use it.

A: Its a general "catch-all" for additional data you wish to store with a control.
I too have never used  it.

A: We perform heavy use of tags. We have some methods for checking input, and these methods checks whats in the tags in order to know what control to perform.
IE: if a textbox has RQ=1;DT=int;MAX=100
the automatic method knows that this text can not be left blank, that should accept only integers within 0 and 100.
We have a complete pseudo declarative language for this.
Kind of useful!
More specific for your question, Tags are for your use.

A: for example you have a lot of buttons with single method handling clicks. then at handler you have do differentiate them from each other. So you put some sort of id (or reference) and then access it there.

A: It allows you to store some of your own data with a control. It mostly useful in tree controls where you might want each node/leaf to have some extra data associated with it. This way when you click on a node you can perform an action relevant to the node.

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text:
Home All issues Volume 598 (February 2017) A&A, 598 (2017) A1 Abstract
Extragalactic astronomy
A&A 598, A1 (2017)
[Ultra] luminous infrared galaxies selected at 90 μm in the AKARI deep field: a study of AGN types contributing to their infrared emission⋆
K. Małek1, M. Bankowicz2, A. Pollo1,2, V. Buat3, T. T. Takeuchi4, D. Burgarella3, T. Goto5, M. Malkan6 and H. Matsuhara7
1 National Centre for Nuclear Research, ul. Hoża 69, 00-681 Warszawa, Poland
e-mail: Katarzyna.Malek@ncbj.gov.pl
2 The Astronomical Observatory of the Jagiellonian University, ul. Orla 171, 30-244 Kraków, Poland
3 Laboratoire d'Astrophysique de Marseille, OAMP, Université Aix-Marseille, CNRS, 38 rue Frédéric Joliot-Curie, 13388 Marseille Cedex 13, France
4 Department of Particle and Astrophysical Science, Nagoya University, Furo-cho, Chikusa-ku, 464-8602 Nagoya, Japan
5 Dark Cosmology Centre, Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, 2100 Copenhagen, Denmark
6 Department of Physics and Astronomy, University of California, Los Angeles, CA 90024, USA
7 Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, Sagamihara, 229-8510 Kanagawa, Japan
Aims. The aim of this work is to characterize physical properties of ultra luminous infrared galaxies (ULIRGs) and luminous infrared galaxies (LIRGs) detected in the far-infrared (FIR) 90 μm band in the AKARI Deep Field-South (ADF-S) survey. In particular, we want to estimate the active galactic nucleus (AGN) contribution to the LIRGs and ULIRGs' infrared emission and which types of AGNs are related to their activity.
Methods. We examined 69 galaxies at redshift ≥0.05 detected at 90 μm by the AKARI satellite in the ADF-S, with optical counterparts and spectral coverage from the ultraviolet to the FIR. We used two independent spectral energy distribution fitting codes: one fitting the SED from FIR to FUV (CIGALE) (we use the results from CIGALE as a reference) and gray-body + power spectrum fit for the infrared part of the spectra (CMCIRSED) in order to identify a subsample of ULIRGs and LIRGs, and to estimate their properties.
Results. Based on the CIGALE SED fitting, we have found that LIRGs and ULIRGs selected at the 90 μm AKARI band compose ~56% of our sample (we found 17 ULIRGs and 22 LIRGs, spanning over the redshift range 0.06 <z< 1.23). Their physical parameters, such as stellar mass, star formation rate (SFR), and specific SFR are consistent with the ones found for other samples selected at infrared wavelengths. We have detected a significant AGN contribution to the mid-infrared luminosity for 63% of LIRGs and ULIRGs. Our LIRGs contain Type 1, Type 2, and intermediate types of AGN, whereas for ULIRGs, a majority (more than 50%) of AGN emission originates from Type 2 AGNs. The temperature-luminosity and temperature-mass relations for the dust component of ADF–S LIRGs and ULIRGs indicate that these relations are shaped by the dust mass and not by the increased dust heating.
Conclusions. We conclude that LIRGs contain Type 1, Type 2, and intermediate types of AGNs, with an AGN contribution to the mid infrared emission at the median level of 13 ± 3%, whereas the majority of ULIRGs contain Type 2 AGNs, with a median AGN fraction equal to 19 ± 8%.
Key words: galaxies: active / infrared: galaxies / galaxies: statistics / galaxies: Seyfert
Full Table A.1 is only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/598/A1
Population synthesis modelling of luminous infrared galaxies at intermediate redshift
Properties of star forming galaxies in AKARI Deep Field-South
HELP: modelling the spectral energy distributions of Herschel detected galaxies in the ELAIS N1 field
The physical properties of Spitzer/IRS galaxies derived from their UV to 22 μm spectral energy distribution
Constraining the properties of AGN host galaxies with spectral energy distribution modelling


Mom invited me over for a baked potato bar tonight with the girls. Very good.
I got a very funny, if unexpected, email at work today. The manager of the development group made a mistake on one of our systems and sent me an email to ask me to fix it. So I did and sent her an email telling her it was done.
"Thanks, Sorry for the incontinence."
"Wow - I've got to check my use of spell check... Ahem. I meant to say - sorry for the inconvenience..... ;-) "
I got a good laugh out of it though.
Finished listening to the library book on tape Dark Guardian by Christina Feehan. Romance. Very good.
LOL!!!!!!!!!!!!! now that is funny! spellchecking and proof reading (one word or two?) are totally different!
People make that mistake at my job ALL the time...luckily I catch it before it heads out to a customer!
At least she didn't mean "incompetence"


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Intelligent future: Putting the AI in IoT
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AI is becoming an essential part of IoT deployments, creating opportunities for players across the mobile ecosystem, finds Kate O'Flaherty.
The vast number of connections and devices comprising the IoT continues to surge. At the end of 2018, there were an estimated 22 billion IoT devices in use around the world, according to Statistica. By 2030, it is expected this number will reach around 50 billion.
To unlock IoT's true value, though, the huge amounts of data produced by these connected devices needs to be analysed and acted upon. AI, and in particular the most common variety of it currently in use, machine learning, is key to that unlocking: it can increase efficiency and cut costs across myriad IoT applications, from industrial IoT (IIoT) to healthcare and autonomous vehicles.
AI is already deployed in many IoT ecosystems, but it will become ever more widely used, especially as 5G and edge computing start to emerge. Dr Richard Benjamins, Chief AI and Data Strategist at Telefónica, explains that some of this value comes from predictive analytics, to which AI can be applied. Examples include predictive maintenance to reduce unscheduled downtime and improve safety.
Benedetto Pietrabella, VP of the Americas Network Equipment Providers Business at Altran, a Capgemini company, agrees. He points out that in the past humans could monitor situations, identify problems and react, but this task is now increasingly being passed to a machine learning algorithm. Among the benefits of this approach are, he says, that "It can identify issues early and even predict the month when a piece of equipment will fail."
Martin Garner, an IoT Analyst at CCS Insight, notes, "There's a lot that can be done without AI, but IoT systems are becoming complex and the volumes of data are growing at a rapid rate. We are moving into an era where we need AI to make the most of the data and to cope with the sheer volume of it."
AI use cases in IoT
The use cases for AI in IoT span many sectors. Telefónica, for example, says Dr Benjamins, uses AI to perform predictive maintenance for its industrial clients. The company is also using AI to perform predictive maintenance for connected cars, as well as to detect anomalies in consumption in energy IoT.
Most AI in commercial use is achieved by some form of machine learning, says Dr Benjamins. "Machine learning recognises patterns in massive amounts of data and is able to 'learn' that certain patterns in photos correspond to cats, faces or specific cancers."
John Vickery, Principal Technology Partner for Enterprise at BT, says the operator is using AI in IoT to offer "tangible business benefits" for customers.
BT is working on a 5G IoT deployment in Belfast Harbour (see main picture), where it is testing use cases, including environment monitoring. "A lot of grain and coal is shipped there and stored before it moves on," says Vickery. "We need to think about air quality, public safety and people and things, and how to monitor the air quality so it's safe for the public and employees.
"You can then start to combine different data sources such as CO2 sensors with weather predictions and business intelligence. Rather than taking a snapshot, it's on a real-time basis. It means you can understand at any time what the air quality is like and also start to predict how that might change in certain areas."
Another BT project, in the Forth Valley, uses sensors, satellite data and AI to ascertain water quantity and quality. "We can start to combine data sources to understand the water: is it safe now and will it be in the future?" Vickery says.
He adds that the benefits of AI in IoT include cost efficiency, quality improvements, safety and "insights as a business to help you make strategic decisions".
Industrial scenarios
In industrial scenarios, AI is allowing manufacturers to introduce computer vision and sensor-based technology to improve quality control, and enable the deployment of advanced operational technology such as collaborative robotics, says Dan Jelfs, SVP of Sales, Mobica.
The technology is also enabling production managers to develop prediction failure models and carry out impact analysis. Jelfs explains, "This allows preventative maintenance, process optimisation and the elimination of unnecessary downtime."
It's clear the area is gathering pace. Most vertical industries have started to use AI in some form in IoT, says Jesper Rooth, Director, Solution Architecture, Telecommunications, Red Hat. For example, he says, "Many manufacturing companies want to move away from Wi-Fi on the factory floor to either Wi-Fi6 or 5G to connect industrial devices with sensors.
"The telemetry information from these devices is analysed to build patterns and provide proactive resolutions. Many IoT sensors now have 5G or LTE chipsets and use service provider networks to take advantage of low latency. In many cases, AI is being used with analytics in closed loop automation to analyse and correlate information to perform predictive maintenance."
One major application that takes advantage of AI is the ability to predict failure of service on IoT and embedded devices, says Rooth. For example, some healthcare companies are collecting data from medical equipment in patients' homes. He says, "They use AI to remotely monitor equipment for conditions such as humidity, temperature and battery life. In some cases, AI has helped them to predict if the IoT devices were close to an open window, which could ruin the calibration."
Remote maintenance, exoskeletans
Meanwhile, BICS' customers are using AI in IoT for use cases including remote maintenance and exoskeletons, says Fernando Llobregat, Head of Enterprise Sales and Go-to-Market for IoT, BICS.
The other aspect of AI in IoT that he notes is being used by carriers such as BICS is the measurement of devices' connectivity and behaviour on the network. "We extract patterns from the usage, which is valuable data as we have devices communicating with different technologies.
"For example, devices switch from the 3G network to 4G depending on coverage and they also switch from country to country. So the data we extract and analyse is very useful to see what's going on. We can detect, for example, when devices are behaving in a strange way, which could mean they are being attacked."
Challenges in AI in IoT
The potential is huge, but there are also challenges in utilising AI within IoT. Access to data can be a major issue, says Dr Benjamins. "There are important discussions going on about who owns IoT data. For instance, in connected cars, is it the manufacturer, the seller or the owner?" Another vexed issue, he adds, is having the right skills to unleash the value of data generated by IoT as these are in short supply.
At the same time, says BT's Vickery, there are commercial challenges. Smart city solutions are a good example. He asks, "You have a big ecosystem of public and private sector customers: who pays for it and how do they monetise it?"
For mobile operators to monetise IoT, they need expertise, says Sef Tuma, Global Lead for Industry X Intelligent Products and Platforms at Accenture. "Benefiting from AI in IoT requires deep understanding of the intent of the industry solution and the context that comes from the data."
Meanwhile, privacy is an important consideration where IoT connects with people's data in areas such as connected cars, says Dr Benjamins.
Managing security is also a problem. Pietrabella warns, "In metropolitan use cases when you are monitoring for safety, cameras can be stolen or hijacked. The IoT environment by nature is not secure."
There are obstacles to be overcome, but one thing is certain: in the future, AI will be an essential part of IoT deployments. "Applying IoT without using AI and machine learning might solve a concrete business problem, but this leaves a significant amount of value untapped," points out Dr Benjamins.
The two technologies will not exist alone. Further down the line, privacy-enhancing technologies (PET), 5G, cloud and blockchain will also become a key part of AI in IoT.
The roll out of 5G and edge computing will help AI applications reach mainstream adoption, as it will enable inferences to be made much faster, says Jelfs. "The 5G standard, which enables network slicing to allow use cases such as massive machine-type communications, should reduce latency by 50 times and increase bandwidth by four times."
Meanwhile, he says edge computing will result in compute processing taking place locally. "This will further reduce latency and the potential bottlenecks that can slow cloud computing response times." In scenarios where microseconds make a difference, such as managing the pressure in industrial pipes, this can be crucial, says Jelfs.
As the IoT landscape continues to grow and diversify, the need for AI will become even greater. On the connectivity side, 5G could be transformative by adding useful data to provide visibility into what is happening in the network. "5G will have the capabilities to apply machine learning algorithms to other data, such as signalling information, which will provide a better view into security," notes Llobregat.
This will be critical in autonomous vehicles, where security is required in the car itself and at the connectivity level, he says. "In the future, it will be important that all the people participating in the connectivity and services – including mobile operators – have visibility into what is going on."
5G	Internet of Things	Artfical intelligence (AI)	Telefónica	Red Hat	BICS	Edge computing	Capgemini	Industry 4.0	IIoT	BT Enterprise	Mobica	Altran


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Home » Topics » Hematology and Oncology » Lymphadenopathy and Splenomegaly: Approach and Evaluation
Causes and Differential Diagnosis of Lymphadenopathy
Causes and Differential Diagnosis of Splenomegaly
Symptoms and History in the Patient with Lymphadenopathy or Splenomegaly
Examination and Signs in the Patient with Lymphadenopathy and Splenomegaly
Investigating and Diagnosing the Patient with Lymphadenopathy and Splenomegaly
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Splenomegaly is often a focus of short case examinations since many of its causes are chronic. Lymphadenopathy may be localized or generalized.
Localized lymphadenopathy
Consider which structures have lymphatic drainage to the nodes affected and examine these carefully for the following:
Local infection: bacterial (e.g., otitis media, tuberculosis) or viral.
Metastases: local malignancy.
Lymphoma: Hodgkin's disease or non-Hodgkin's lymphoma.
Causes of Localized Lymphadenopathy
Generalized lymphadenopathy
Infection: particularly viral (Epstein-Barr virus [EBV], cytomegalovirus [CMV], human immunodeficiency virus [HIV], rubella), but also bacterial (tuberculosis [TB], syphilis, brucellosis) and protozoal (toxoplasmosis).
Lymphoproliferative: Hodgkin's disease or non-Hodgkin's lymphoma, chronic lymphocytic leukemia, acute lymphoblastic leukemia.
Connective tissue disorders: systemic lupus erythematosus, rheumatoid arthritis.
Infiltration: sarcoidosis.
Drugs: phenytoin ("pseudolymphoma").
Endocrine: thyrotoxicosis (rare).
Causes of Diffuse Lymphadenopathy
In general, different diseases cause different degrees of splenomegaly, as follows.
Massive splenomegaly is caused by:
Chronic myeloid leukemia.
Myelofibrosis.
Malaria: rarely.
Kala azar (leishmaniasis, caused by a parasite transmitted by the sand fly): rarely.
Moderate splenomegaly is caused by all of the above plus:
Portal hypertension.
Lymphoproliferative disorders (see above).
Acute leukemias.
Just palpable splenomegaly is caused by all of the above plus:
Infection: infectious mononucleosis, infectious hepatitis, subacute bacterial endocardititis, TB, brucellosis, schistosomiasis.
Hemolytic anemias.
Immune thrombocytopenias.
Connective tissue disease: SLE, rheumatoid arthritis.
Infiltration: amyloid, sarcoid.
Storage disorders: Gaucher's disease.
Myeloproliferative disorders: polycythemia rubra vera, essential thrombocythemia.
Megaloblastic anemias.
Splenomegaly – causes
Causes of Splenomegaly Grouped by Pathogenic Mechanism
It is often not possible to make a diagnosis on the basis of the history in these patients. However, important clues in the history can help to focus the clinical examination and further investigations.
Symptoms and History in Localized lymphadenopathy
Rate of node enlargement
Lymphadenopathy associated with infection often develops quickly and may be painful. When due to lymphoma or malignancy, the rate of enlargement tends to be slower and can wax and wane in the case of lymphoma. Sometimes the lymphadenopathy will not be noticed until it becomes large and causes disfigurement or rubs against clothes.
Lymphadenopathy may also result in lymphedema. This is a nonpitting edema caused by blockage of the lymph channels. Lymphedema may be the presenting sign of lymphadenopathy as the increasing size of the lymph nodes cuts off flow of regional lymph channels.
Symptoms in local structures
Has the patient noticed pain, erythema, or a mass in any of the structures draining into the affected node (e.g., cellulitis in inguinal lymphadenopathy or a breast mass in axillary lymphadenopathy)?
Systemic symptoms
In lymphoma the patient may experience "B symptoms" (fever, night sweats, weight loss), which indicate a poorer prognosis.
Symptoms and History in Generalized lymphadenopathy
A full systemic inquiry is essential in these patients as most of the causes of generalized lymphadenopathy can affect multiple systems. Special attention should be paid to the following:
Malaise, anorexia and general debility: common but nonspecific.
"B symptoms": hematologic malignancy.
Ask about tender lymph nodes after consumption of alcohol (can be seen in Hodgkin's disease).
Skin rash: rubella, SLE, and sarcoidosis.
Arthragia and arthropathy: SLE, rheumatoid arthritis, syphilis (Charcot's joints).
Infectious contacts: rubella, TB, and EBV.
Risk factors for HIV infection
Drug history: to exclude phenytoin or beryllium as a cause. Also ask about any history of IV drug use.
Symptoms of thyrotoxicosis: heat intolerance, weight loss, increased appetite, diarrhea, irritability.
Symptoms and History in Splenomegaly
Previous medical history
Is the patient known to have a pre-existing illness that can cause splenomegaly, such as chronic liver disease resulting in portal hypertension, connective tissue disease, thalassemia (hemolysis), Gaucher's disease, or damaged cardiac valves (rheumatic fever or prosthetic valve) with subacute bacterial endocarditis?
Recent travel abroad or infectious contacts
Consider infectious mononucleosis, TB, schistosomiasis, and malaria.
Systemic symptoms suggestive of an underlying cause include arthralgia, rash, and "B symptoms" (as above).
Symptoms of hematologic disturbance
Anemia may be present due to marrow infiltration, chronic disease, hemolysis, vitamin deficiency, or hypersplenism.
Leukopenia causing recurrent infections may result from marrow infiltration, hypersplenism, or infection.
Thrombocytopenia may be due to immune platelet destruction, marrow infiltration, or hypersplenism.
When lymphadenopathy or splenomegaly is present, a full clinical examination of the lymphatic system should be made. The examination should then focus on possible underlying causes
Examining the patient with lymphadenopathy and splenomegaly
Which lymph nodes are affected?
Firstly, the extent, sites, sizes, consistency, tenderness, and fixation of enlarged lymph nodes should be documented. Cervical, occipital, supraclavicular, axillary, and inguinal areas should be palpated carefully.
Normal reactive nodes are generally less than 1 cm in diameter, feel soft, are not fixed, and can be tender.
Lymphomatous nodes are often larger and feel rubbery but are not fixed.
Lymph nodes infiltrated by carcinoma feel hard and may be fixed to surrounding tissue.
Is there splenomegaly?
If splenomegaly is present, the size (in cm) from the left costal margin must be recorded. It is important to distinguish the left kidney from the spleen when palpating a mass in the left hypochondrium and the differences between the two are commonly asked for in examinations (see Image bellow). A palpable spleen is at least twice its normal size.
Characteristic clinical features which distinguish between the spleen and left kidney
Is there evidence of an underlying cause?
Anemia and purpura may be present as described above.
Jaundice may result from chronic liver disease, hemolysis, or infective hepatitis.
Cachexia heralds underlying malignancy.
Needle marks may indicate previous exposure to HIV and hepatitis B or C or provide a source of bacteria in infective endocarditis.
Additional clinical features of some conditions presenting with splenomegaly
Examine those structures with lymphatic drainage to the affected nodes. Erythema, increased temperature, and tenderness suggest infection, while a hard, nontender mass may indicate malignancy. When there is isolated cervical lymphadenopathy, a formal ear, nose, and throat examination should also be performed since oropharyngeal malignancies commonly metastasize to these nodes.
Splenomegaly and generalized lymphadenopathy
Where there is both splenomegaly and generalized lymphadenopathy consider lymphoproliferative disorders, infection, connective tissue disease, and sarcoidosis.
Algorithm for diagnosis in the patient with lymphadenopathy and splenomegaly
A complete blood count may show anemia, leucopenia, thrombocytopenia, or a combination of these.
Blood film can provide diagnostic information (see Image bellow).
Erythrocyte sedimentation rate will be elevated in infection, malignancy, and inflammation.
Bone marrow examination includes aspiration, trephine, and cytogenetic analysis. It is indicated if the blood count or film suggest hematological abnormalities, and it is useful in the diagnosis of leukemias, myeloproliferative disorders, immune thrombocytopenias, and pancytopenia. Occasionally it is helpful in storage diseases, lymphoma, and carcinoma, where there is marrow infiltration.
Blood film abnormalities in conditions presenting with lymphadenopathy and splenomegaly
Liver function tests:
transaminases will be abnormal in infective hepatitis and sometimes in EBV and CMV;
elevation in alkaline phosphatase and γ-glutamyl transpeptidase will occur when the porta hepatis is obstructed by enlarged lymph nodes;
unconjugated hyperbilirubinemia will be present in hemolysis;
an elevated lactate dehydrogenase indicates a poor prognosis in lymphoma.
Serum calcium: raised in malignancy, sarcoidosis, and sometimes lymphoma.
Serum uric acid: raised when there is rapid cell turnover such as in malignancy.
Thyroid function tests: thyrotoxicosis.
Infection screen
Monospot test: EBV.
Serology: EBV, CMV, HIV, rubella, hepatitis, toxoplasmosis, and brucellosis.
Blood cultures: repeated if infective endocarditis is suspected.
Sputum culture: TB.
Differential diagnosis of fever and splenomegaly
Autoantibody screen
This is useful in the detection of connective tissue disord.
Chest x-ray: bilateral hilar lymphadenopathy (caused by lymphoma, sarcoidosis, and TB).
Abdominal ultrasound scan: will confirm the presence of splenomegaly.
Computed tomography scan of the chest, abdomen, and pelvis: gives clear staging information in malignancy and particularly lymphoma where retroperitoneal lymphadenopathy may often be missed by ultrasound scan.
MRI can evaluate intra-abdominal lymph nodes, look for a primary malignancy, and determine whether masses are cystic.
Previous PostAnemia: Approach and Evaluation
Anticoagulants and Fibrinolytics – Summary
Vaso-Occlusive Episode (VOE) in Sickle Cell Disease


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Tag Archives: but not justice…
Finally – resolution on prior authority!!!! (sort of, but not really)
Posted on May 31, 2012 by suesspiciousminds
Our beloved President (and honestly, no sarcasm here, I am delighted!) has finally tackled the Prior Authority issue.
http://www.bailii.org/ew/cases/EWHC/Fam/2012/1442.html
In DS & Ors (Children) 2012. (Am a little sad that I didn't get to be the one who got to run the case, having expended quite some time on the issue, but delighted that it is finally gripped)
Interestingly, the President takes a different view to me on whether the LSC have law on their side here.
Para 38 For present purposes, the law can be taken quite shortly. To the mind of the lawyer it remains curious that an administrative body can effectively render nugatory a judicial decision taken in what the court perceives as the best interests of a child. Where the party or parties who seek to instruct an expert are publicly funded, however, there is no doubt that the LSC has the power, given to it by Parliament, to refuse to fund the instruction or to fund the instruction in part only. Moreover, the LSC undoubtedly has the power, deriving from the same source, to cap the level of fees which may be expended by the expert at a given level. That is undoubted the law. Lawyers may complain that this is an unfair state of affairs, or that they cannot find experts who will work at the rates laid down. Their remedy, if they take the view that the decision of the LSC is Wednesbury unreasonable or can be struck down for any other public law reason, is to apply for judicial review.
If I recall correctly, both Calderdale and Lambeth (the cases I think mean that the Court takes precedence over the LSC internal policies) are both High Court, so the President is not bound by them, and distinguishes them in any event by saying that the Statutory Instrument which sets out how the LSC have capped expert fees is binding. (In my humble opinion, it would be binding, had the draftsmen remembered to put something into the SI that said that it was binding on the Courts, but such is life). A closer inspection of this authority shows that Justice Wall specifically refers to Calderdale on the issue of splitting costs, so I am certain that the argument that the Court pushes the LSC around, not vice versa, is, I'm afraid over. And we lost.
The law, as it stands then, is that the LSC DO have the power to bind the Court, and Mr Justice Wall suggests that the remedy is a judicial review if the LSC are acting in a Wednesbury unreasonable way. Presumably, the LA as a body with locus standi, could launch that JR if the LSC decision was delaying a case, because heaven knows the last thing a publicly-funded solicitor who depends on the LSC to process claims and write cheques wants to do is hack off the paymaster.
Here is some very helpful concrete guidance – as much of it places onerous tasks on the Judge/Magistrates if granting approval for an expert, expect to have a harder task over the next few weeks in getting an expert past the Court.
In all the circumstances of this case, therefore, I feel able to offer the following general guidance:-
i) The words "the cost thereof is deemed to be a necessary and proper disbursement on [a named individual's] public funding certificate" (or words to equivalent effect) should no longer be used when the court orders a report from an expert. The words do not bind the LSC or, for that matter anybody else. In addition, there must be doubt about the court's power to make such an order. It is, in my judgment, far better to follow the words of the Regulations, particularly if the court is being asked to approve rates in excess of those allowed by the Funding Order. A copy of such an order is attached at the end of this judgment.
ii) The test for expert evidence will shortly import the word "necessary". The question which the court will have to ask itself is whether or not the report of the expert is necessary for the resolution of the case. FPR rule 25.1 will shortly be amended to insert the word "necessary" for "reasonably required" and there will be a new Practice Direction.
iii) It is the court which makes the order for the instruction of an expert, and this responsibility neither can nor should be delegated to the parties. It is of the essence of good case management that the court should identify the issues on which it wants the expert to report. It would thus be helpful and important for the tribunal to be able to say – if it is the case and the hard pressed Tribunal with a long list has had the time – that it has read all the (relevant) papers.
iv) If the court takes the view that an expert's report is necessary for the resolution of the case, it should say so, and give its reasons. This can be done by a preamble to the order, or by a short judgment, delivered at dictation speed or inserted by the parties with the judge's approval. I have considered this point carefully, and have come to the conclusion that this does not impose an undue burden either on the court or the profession.
v) There is no substitute for reasons. A consent order is still an order of the court: it is a judicial decision and must be supported by reasons. Equally, a decision by the LSC is a decision. It too should be supported by reasons.
vi) "Reasons" in circumstances such as these need not be lengthy or elaborate. They must, however, explain to anyone reading them why the decision maker has reached the conclusion he or she has particularly if the expert is seeking to be paid at rates which are higher than those set out in the table in Schedule 6 of the Funding Order
vii) Speed is of the essence in proceedings relating to children. An application for prior authority must be made at the earliest opportunity and, once again, must be carefully drafted and supported by reasons.
viii) By like token, it behoves the LSC to deal with such applications promptly and, particularly if the application is being refused, or only granted to a limited extent, to give its reasons for its decision. Once again, the reasons can be concise. Of course the solicitor seeking prior authority can go ahead regardless, and instruct the expert at the rates the expert demands, but such a suggestion, in reality, is unreal. The expert's contract is with the solicitor, and if he or she does not recover the expert's costs from the LSC, it is the solicitor who is liable. Given the exiguous rates of remuneration, this is a risk no solicitor is willing to take, particularly where the client is impecunious.
ix) Similar considerations to those set out above apply to any challenge to the LSC's ruling.
x) If a case is urgent, it should be so marked and the reasons for its urgency explained.
xi) Courts should familiarise themselves with Part 25 of the FPR and with Practice Direction 25A which supplements it. Specifically, they should be aware of paragraph 4.3(h) or its equivalent when amended which provides that the person wishing to instruct an expert must explain to the court why the expert evidence proposed cannot be given by Social Services undertaking a core assessment or by the Children's Guardian in accordance with their respective statutory duties. The Rule and the Practice Direction are being revised to make them (it is to be hoped) more practical and "user friendly". Practitioners should look out, in due course, for the amendments.
And then a suggested form of wording for orders (you will note that this is a LOT longer at present, and the President stresses that all of this should be prefaced by a short judgment as to why the expert is required, and at the minimum a clear preamble that sets out why the judicial decision has been made)
A suggested form of order, depending on the facts of the individual case, could be in the following terms: –
a) The proposed assessment and report by X (as set out in paragraph 2 of this order) are vital to the resolution of this case.
b) This case is exceptional on its facts.
c) The costs to be incurred in the preparation of such reports are wholly necessary, reasonable and proportionate disbursement on the funding certificates of the publicly funded parties in this case.
d) The court considers X's hourly rate of £y and the estimated costs of the assessment report to be reasonable in the context of (his) qualifications, experience and expertise.
e) The field in which X practises, and the particular expertise which (he) brings to bear on cases involving (subject) are highly specialised. There is no realistic prospect of finding an alternative expert with the necessary expertise at lower fee.
f) (The court considers that any further delay in order to give the LSC the (further) opportunity to consider an application for prior authority to incur the costs of the proposed amendment or report would be wholly outside the child(ren's) timescale(s).
Even such an order (which will need, of course, to be adapted to the facts of the individual case) should be buttressed by reasons as set out in the guidance which I have attempted to give.
There's a very interesting addendum to the judgment, where the LSC submitted some data to the Court. Here are the figures on applications for prior authorities :-
Nov 2011 – 216
Dec 2011 – 492
Jan 2012 – 784
Feb 2012 – 1140
Mar 2012 – 1840
I wonder why the numbers spiked so – might it be because the LSC started rejecting claims left right and centre, leaving solicitors holding the baby and being out of pocket and thus deciding never to get burned like that again?
Laughably, they also claim to be processing prior authority applications in between 3 and 8 days. (Perhaps, if their definition of a Day is the time it takes Jupiter to orbit the sun)
So, where are we? I suspect, still waiting for the judicial review. The white flag has been waved by the Courts as to whether they or the LSC are in charge of assessments, so what Justice Wall has done here is set out a clear framework in advance for prior authority applications to be accompanied by chapter and verse on why the Court has decided that the assessment is necessary and the costs appropriate. That paves the way, should the LSC act capriciously (as if they ever would, quell my scepticism) for a judicial review.
If you're an Independent Social Worker, this case is really, really bad news, I'm afraid. The Courts are not going to do battle with the LSC in any care case as to the ludicrous £30 per hour cap that was pulled out of thin air. It will have to be a judicial review based on the policy being unreasonable and having been done without an Impact assessment. (And I think the clock has chimed on the time-limit for such an application – unless the applicant (Nagalro, or BASW presumably) argues that it was unclear until this decision that the intention was to bind the courts, or that social workers doing risk assessments would not get the £63 per hour that the SI suggests)
Posted in case law, experts, family justice modernisation and tagged but not justice..., expert, prior authority, really really long orders, resolution. Bookmark the permalink.


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July 22, 2015 Fact of the Day: With increased net worth, who pays the bills? Men or Women?
DID YOU KNOW THAT AS NET WORTH INCREASES, MEN BECOME MORE LIKELY TO TAKE RESPONSIBILITY FOR PAYING THE HOUSEHOLD BILLS?
In households with $1MM or less in net worth, 30% of husbands say they pay the bills. But in households with $5MM or more, 45% of husbands indicate they pay the bills.
But who pays the bills also depends on how much people know about investing. For those who are very knowledgeable about investing, 48% of husbands pay the bills, and 19% say the wife does. In contrast, among those who know little about investing, only 23% say the husband pays the bills, while 42% say the wife does. So who pays the bills seems dependent on a lot of different factors. Who pays the bills in your house?
But more important than WHO pays the bills is being able to pay the bills. And paying bills is less stressful when you know that you will be able to meet your obligations in the future.
To learn more about High Income women click here or contact Randy Wostratzky at rwostratzky@spectrem.com or 224-544-5195.