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From the Dirac equation of an electron in an anisotropic conduction band, the anisotropy of its motion dramatically affects its interaction with applied electric and magnetic fields. The quantum spin Hall effect (QSHE) is observable in two-dimensional metals without spin-orbit coupling. The dimensionality of the Zeeman interaction plays an important role in the QSHE, and profoundly modifies many interpretations of measurements of the Knight shift and of the upper critical field in highly anisotropic superconductors.

We extend the Anderson impurity model to a large-spin Fermi system with spin $f$=3/2, stimulated by the realization of large-spin ultracold Fermi atoms. The condition required for the spontaneous formation of local magnetic moments is examined and the ground state mean-field magnetic phase diagram is explored carefully. We find that the spin-3/2 Fermi system involves magnetic phase regions I, II, and III that correspond to one, two, and three particle/hole occupation, respectively. In addition, it is observed that all the three magnetic phases have four-fold degenerate ground states. Finally, the phase transition between the three phases seems to be of the first-order., Comment: 9 pages, 13 figures

The Dirac equation is extended for a relativistic electron in an orthorhombically-anisotropic conduction band. Its covariance is established with general proper and improper Lorentz transformations. In the non-relativistic limit, the kinetic and Zeeman energy terms of the Hamiltonian are both determined by the same three effective masses, and the quantum spin Hall effect is derived. This has important consequences for magnetic measurements of many classes of clean anisotropic semiconductors, metals, and superconductors. The Zeeman energy is vanishingly small for magnetic fields parallel to clean monolayers and in all directions in quasi-one-dimensional materials., Comment: 5 pages, 0 figures

We compute the quantum information metrics of a thermal CFT on $\mathbb R^{1,1}$ perturbed by the scalar primary operators of conformal dimension $\Delta=3,4,5,6$. In particular, we assume that the Hamiltonian of the mixed state commutes with each other and the temperature is fixed. Under these conditions, the evaluation is analogous to the pure state case. We also apply the method of [arXiv:1607.06519] to calculate the mixed state information metric for the scalar primary operator with conformal dimension $\Delta=4$ holographically. We find an exact agreement between the two results in our approach., Comment: 13 pages, no figures. Comments are welcome. Title corrected

Annihilation process of a pair of vortices in holographic superfluid is numerically simulated. The process is found to consist of two stages which are amazingly separated by vortex size $2r$. The separation distance $\delta(t)$ between vortex and anti-vortex as a function of time is well fitted by $\alpha (t_{0}-t)^{n}$, where the scaling exponent $n=1/2$ for $\delta (t)>2r$, and $n=2/5$ for $\delta(t)<2r$. Then the approaching velocity and acceleration as functions of time and as functions of separation distance are obtained. Thus the attractive force between vortex and anti-vortex is derived as $f(\delta)\propto 1/\delta^{3}$ for the first stage, and $f(\delta)\propto 1/\delta^{4}$ for the second stage. In the end, we explained why the annihilation rate of vortices in turbulent superfluid system obeys the two-body decay law when the vortex density is low., Comment: 14 pages, 5 figures

Effects of Lovelock gravity on the Joule-Thomson expansion are probed from various perspectives. The well-known Joule-Thomson coefficient is derived with both the explicit expression and intuitive image presented. Moreover, the inversion curves showing the relation between the inversion temperature and the inversion pressure are studied. It is shown that for given inversion pressure, the inversion temperature of the case $\alpha\neq0$ ($\alpha$ is the Lovelock parameter) is much lower than that of the case $\alpha=0$. And the inversion temperature tends to decrease with $\alpha$, in contrast to the effect of the electric charge. It is also shown that the ratio between the minimum inversion temperature and the critical temperature decreases with $\alpha$ for $\alpha\neq0$. Furthermore, the isenthalpic curves are investigated with rich physics revealed. The intersection point between the isenthalpic curve and the inversion curve is exactly the inversion point discriminating the heating process from cooling process. It is shown that both the inversion temperature and the inversion pressure for $\alpha\neq0$ are much lower for the same given mass of the black hole, showing the effect of Lovelock gravity. Last but not the least, we discuss the case of uncharged Lovelock AdS black holes with interesting feature found. It is shown that the Joule-Thomson coefficient is always positive, suggesting the expansion is always in the regime of cooling process. And no inversion temperature exists, in contrast to the case $Q\neq0$. Isenthalpic curves are also quite different since the temperature increases monotonically with the pressure when the mass is specified., Comment: 14pages,5figures

The topological charge $\epsilon$ of AdS black hole is introduced in Ref.[1,2], where a complete thermodynamic first law is obtained. In this paper, we investigate a new phase transition related to the topological charge in Einstein-Maxwell theory. Firstly, we derive the explicit solutions corresponding to the divergence of specific heat $C_{\epsilon}$ and determine the phase transition critical point. Secondly, the $T-r$ curve and $T-S$ curve are investigated and they exhibit an interesting van der Waals system's behavior. Critical physical quantities are also obtained which are consistent with those derived from the specific heat analysis. Thirdly, a van der Waals system's swallow tail behavior is observed when $\epsilon>\epsilon_{c}$ in the $F-T$ graph. What's more, the analytic phase transition coexistence lines are obtained by using the Maxwell equal area law and free energy analysis, the results of which are consistent with each other., Comment: 11 pages, 5 figures

Effects of the dimensionality on the Joule-Thomson expansion are discussed in detail by considering the case of $d$-dimensional charged AdS black holes. Specifically, we investigate three important aspects characteristic of the Joule-Thomson expansion. Namely, the Joule-Thomson coefficient, the inversion curves and the isenthalpic curves. We utilize two different approaches to derive the explicit expression of the Joule-Thomson coefficient and show that both approaches are consistent with each other. The divergent point and the zero point of the Joule-Thomson coefficient are discussed. The former is shown to reveal the information of Hawking temperature while the latter is depicted through the so-called inversion curves. Fine structures of the inversion curves are disclosed in the cases $d>4$. At low pressure, the inversion temperature increases with the dimensionality $d$ while at high pressure it decreases with $d$. The ratio between minimum inversion temperature $T_{min}$ and the critical temperature $T_c$ is discussed with its explicit expression obtained for $d>4$. Surprisingly, it is shown that the ratio is not always equal to $1/2$ but decreases with the dimensionality $d$. Moreover, isenthalpic curves of $d>4$ are shown to expand toward higher pressure when the dimensionality $d$ increases., Comment: Comments welcome. 11pages, 5figures

We study the two-dimensional Hubbard model with the Rashba type spin-orbit coupling within and beyond the mean-field theory. The antiferromagnetic ground state for the model at half-filling and the Cooper pairing induced by antiferromagnetic spin fluctuations near half-filling are examined based on the random-phase approximation. We show that the antiferromagnetic order is suppressed and the magnetic susceptibility turns out to be anisotropic in the presence of the spin-orbit coupling. Energy spectrums of transverse spin fluctuations are obtained and the effective interactions between holes mediated by antiferromagnetic spin fluctuations are deduced in the case of low hole doping. It seems that the spin-orbit coupling tends to form s+p-wave Cooper pairs, while the s+d-wave pairing is dominant when the spin-orbit coupling is absent., Comment: 9 pages, 10 figures

The first law of entanglement has been used to obtain the linearized Einstein equations of the holographic dual spacetimes. In the present paper, the first law of entanglement in quasi-topological gravity is explicitly derived by using the Iyer-Wald formalism. In addition, we investigate the extended first law of entanglement for the special case in Quasi-Topological gravity., Comment: 18pages, no figures. A reference is added, the extended first law is discussed in section 4

Heat engine models are constructed within the framework of massive gravity in this paper. For the four-dimensional charged black holes in massive gravity, it is shown that the heat engines have a higher efficiency for the cases $m^2>0$ than for the case $m=0$ when $c_1<0, c_2<0$. Considering a specific example, we show that the maximum efficiency can reach $0.9219$ while the efficiency for $m=0$ reads $0.5014$. The existence of graviton mass improves the heat engine efficiency significantly. The situation is more complicated for the five-dimensional neutral black holes. Not only the $c_1, c_2, m^2$ exert influence on the efficiency, but also the constant $c_3$ corresponding to the third massive potential contributes to the efficiency. When $c_1<0, c_2<0, c_3<0$, the heat engine efficiency of the cases $m^2>0$ is higher than that of the case $m=0$. By studying the ratio $\eta/\eta_C$, we also probe how the massive gravity influences the behavior of the heat engine efficiency approaching the Carnot efficiency., Comment: 9pages,4figures

In this article, a feasible switchyard design is proposed for the Shanghai soft x-ray free electron laser facility. In the proposed scheme, a switchyard is used to transport the electron beam to different undulator lines. Three-dimensional start-to-end simulations have been carried out to research the beam dynamic during transportation. The results show that the emittance of the electron beam increases less than 10%, at meanwhile, the peak current, the energy spread and the bunch length are not spoiled as the beam passes through the switchyard. The microbunching instability of the beam and the jitter of the linear accelerator (linac) are analyzed as well., Comment: 8 pages, 8 figures 2 tables

We revisit the Hawking temperature$-$entanglement entropy criticality of the $d$-dimensional charged AdS black hole with our attention concentrated on the ratio $\frac{T_c \delta S_c}{Q_c}$. Comparing the results of this paper with those of the ratio $\frac{T_c S_c}{Q_c}$, one can find both the similarities and differences. These two ratios are independent of the characteristic length scale $l$ and dependent on the dimension $d$. These similarities further enhance the relation between the entanglement entropy and the Bekenstein-Hawking entropy. However, the ratio $\frac{T_c \delta S_c}{Q_c}$ also relies on the size of the spherical entangling region. Moreover, these two ratios take different values even under the same choices of parameters. The differences between these two ratios can be attributed to the peculiar property of the entanglement entropy since the research in this paper is far from the regime where the behavior of the entanglement entropy is dominated by the thermal entropy., Comment: Comments welcome. 11 pages, 3 figures

We investigate the ratios of critical physical quantities related to the $T-S$ criticality of charged AdS black holes. It is shown that the ratio $\frac{T_cS_c}{Q_c}$ is universal while $\frac{T_cr_c}{Q_c}$ is not. This finding is quite interesting considering the former observation that both the $T-S$ graph and $T-r_+$ graph exhibit reverse van der Waals behavior. It is also worth noting that the value of $\frac{T_cS_c}{Q_c}$ differs from that of $\frac{P_cv_c}{T_c}$ for $P-V$ criticality. Moreover, we discuss universal ratios for the $P-V$ criticality and $Q-\Phi$ criticality. We successfully interpret the former finding that the ratio $\frac{\Phi_cQ_c}{T_c}$ is not universal and construct two universal ratios for the $Q-\Phi$ criticality instead. To the best of our knowledge, we are the first to introduce the dimensional analysis technique to study the ratios of critical physical quantities. It is expected that this technique can be generalized to probe the universal ratios for $Y-X$ criticality in future research.

We analyze an experimentally realizable model of bosons in a zig-zag optical lattice, showing that by rapidly modulating the magnetic field one can tune interaction parameters and realize an analog of the Haldane phase. We explain how quantum gas microscopy can be used to detect this phase's non-local string order and its topological edge states. We model the detection process. We also find that this model can display supersolid correlations, but argue that they only occur at parameter values which would be challenging to realize in an experiment., Comment: 5 pages, 4 figures + supplemental material

We define a kind of heat engine via three-dimensional charged BTZ black holes. This case is quite subtle and needs to be more careful. The heat flow along the isochores does not equal to zero since the specific heat $C_V\neq0$ and this point completely differs from the cases discussed before whose isochores and adiabats are identical. So one cannot simply apply the paradigm in the former literatures. However, if one introduces a new thermodynamic parameter associated with the renormalization length scale, the above problem can be solved. We obtain the analytical efficiency expression of the three-dimensional charged BTZ black hole heat engine for two different schemes. Moreover, we double check with the exact formula. Our result presents the first specific example for the sound correctness of the exact efficiency formula. We argue that the three-dimensional charged BTZ black hole can be viewed as a toy model for further investigation of holographic heat engine. Furthermore, we compare our result with that of the Carnot cycle and extend the former result to three-dimensional spacetime. In this sense, the result in this paper would be complementary to those obtained in four-dimensional spacetime or ever higher. Last but not the least, the heat engine efficiency discussed in this paper may serve as a criterion to discriminate the two thermodynamic approaches introduced in Ref.[29] and our result seems to support the approach which introduces a new thermodynamic parameter $R=r_0$., Comment: Revised version. Discussions added

In this paper, we investigate the thermodynamics of higher-dimensional $f(R)$ black holes in the extended phase space. Both the analytic expressions and numerical results for the possible critical physical quantities are obtained. It is proved that meaningful critical specific volume only exists when $p$ is odd. This unique phenomenon may be attributed to the combined effect of $f(R)$ gravity and conformally invariant Maxwell field. It is also shown that the ratio $P_cv_c/T_c$ differs from that of higher dimensional charged AdS black holes in Einstein gravity. However, the ratio for four-dimensional $f(R)$ black holes is the same as that of four-dimensional RN-AdS black holes, implying that $f(R)$ gravity does not influence the ratio. So the ratio may be related to conformally invariant Maxwell field. To probe the phase transition, we derive the explicit expression of the Gibbs free energy with its graph plotted. Phase transition analogous to the van der Waals liquid-gas system take place between the small black hole and the large black hole. Classical swallow tail behavior, characteristic of first order phase transition, can also be observed in the Gibbs free energy graph. Critical exponents are also calculated. It is shown that these exponents are exactly the same as those of other AdS black holes, implying that neither $f(R)$ gravity nor conformally invariant Maxwell field influence the critical exponents. Since the investigated black hole solution depends on the form of the function $f(R)$, we discuss in detail how our results put constraint on the form of the function $f(R)$ and we also present a simple example., Comment: This paper was firstly submitted to journal on Jan 11th, 2016 and was accepted for publication in EPJC on Sep 19th, 2016