XXZ自旋链中空间非均匀初态的量子猝灭
Quantum Quenches in an XXZ Spin Chain from a Spatially Inhomogeneous Initial State
摘要：
结果提出了量子$XXZ$自旋链的非平衡动力学，其自旋最初安排在畴壁轮廓通过施加磁场的$z$ -方向，这是沿链空间变化。系统被两种方式驱动出平衡：a）。通过快速关闭磁场，b）。通过在关闭磁场的同时快速淬灭相互作用。通过对$XX$链的费米子问题的精确解以及对$XXZ$链的玻色化方法和平均场方法，研究了畴壁轮廓的时间演化以及各种两点自旋关联函数.在长时间的磁化被发现平衡（达到基态值），而两点关联函数一般不。特别地，对于无间隙$XX$相内的猝灭，横向自旋关联函数在长时间内获得空间不均匀结构，其细节取决于初始畴壁轮廓。的空间不均匀性也恢复的情况下，最初安排在畴壁轮廓的经典自旋，并显示的不均匀性出现由于失相的横向自旋分量的畴壁加宽。广义吉布斯系综的方法被发现是不足以捕捉这种空间不均匀的状态。
英文摘要：
Results are presented for the nonequilibrium dynamics of a quantum $XXZ$-spin chain whose spins are initially arranged in a domain wall profile via the application of a magnetic field in the $z$-direction which is spatially varying along the chain. The system is driven out of equilibrium in two ways: a). by rapidly turning off the magnetic field, b). by rapidly quenching the interactions at the same time as the magnetic field is turned off. The time-evolution of the domain wall profile as well as various two-point spin correlation functions is studied by the exact solution of the fermionic problem for the $XX$ chain and via a bosonization approach and a mean-field approach for the $XXZ$ chain. At long times the magnetization is found to equilibrate (reach the ground state value), while the two-point correlation functions in general do not. In particular, for quenches within the gapless $XX$ phase, the transverse spin correlation functions acquire a spatially inhomogeneous structure at long times whose details depend on the initial domain wall profile. The spatial inhomogeneity is also recovered for the case of classical spins initially arranged in a domain wall profile and shows that the inhomogeneities arise due to the dephasing of transverse spin components as the domain wall broadens. A generalized Gibbs ensemble approach is found to be inadequate in capturing this spatially inhomogeneous state.
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