Transport properties of the classical antiferromagnetic XXZ model on the square lattice have been theoretically investigated, putting emphasis on how the occurrence of a phase transition is reflected in spin and thermal transports. As is well known, the anisotropy of the exchange interaction $\mathrm{\ensuremath{\Delta}}\ensuremath{\equiv}{J}_{z}/{J}_{x}$ plays a role to control the universality class of the transition of the model, i.e., either a second-order transition at
TN into a magnetically ordered state or the Kosterlitz-Thouless (KT) transition at
TKT, which respectively occur for the Ising-type ($\mathrm{\ensuremath{\Delta}}>1$) and XY-type ($\mathrm{\ensuremath{\Delta}}<1$) anisotropies, while for the isotropic Heisenberg case of $\mathrm{\ensuremath{\Delta}}=1$, a phase transition does not occur at any finite temperature. It is found by means of the hybrid Monte Carlo and spin-dynamics simulations that the spin current probes the difference in the ordering properties, while the thermal current does not. For the XY-type anisotropy, the longitudinal spin-current conductivity ${\ensuremath{\sigma}}_{xx}^{s}$ ($={\ensuremath{\sigma}}_{yy}^{s}$) exhibits a divergence at
TKT of the exponential form ${\ensuremath{\sigma}}_{xx}^{s}\ensuremath{\propto}exp\left[B/\sqrt{T/{T}_{\text{KT}}\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}\right]$ with
B=O(1), while for the Ising-type anisotropy, the temperature dependence of ${\ensuremath{\sigma}}_{xx}^{s}$ is almost monotonic without showing a clear anomaly at
TN and such a monotonic behavior is also the case in the Heisenberg-type spin system. The significant enhancement of ${\ensuremath{\sigma}}_{xx}^{s}$ at
TKT is found to be due to the exponential rapid growth of the spin-current relaxation time toward
TKT, which can be understood as a manifestation of the topological nature of a vortex whose lifetime is expected to get longer toward
TKT. Possible experimental platforms for the spin-transport phenomena associated with the KT topological transition are discussed.
考虑 decoherence 效果， two-qubit 的纠纷进化各向异性的 Heisenberg XYZ 链面对不同类的磁场被调查。同时发生的时间进化为起始的州的 cos | 被学习 01 +sin | 10 在零温度。纠纷上的不同类的磁场，各向异性的参数和 decoherence 的影响动态详细被探讨，并且稳定的状态的一个同时发生公式被发现。这被显示出纠纷突然的死亡(ESD ) 和纠纷突然的出生(ESB ) 与 decoherence 效果，和稳定的同时发生出现取决于联合力量的一致磁场 B，各向异性的参数和环境，它独立于不同起始的状态和不一致的磁场 b。
The chiral magnetic and chiral separation effects-quantum-anomaly-induced electric current and chiral current along an external magnetic field in parity-odd quark-gluon plasma-have received intense studies in the community of heavy-ion collision physics. We show that analogous effects occur in rotating trapped Fermi gases with Weyl-Zeeman spin-orbit coupling where the rotation plays the role of an external magnetic field. These effects can induce a mass quadrupole in the atomic cloud along the rotation axis which may be tested in future experiments. Our results suggest that the spin-orbit coupled atomic gases are potential simulators of the chiral magnetic and separation effects.