Semiclassical dynamics of a disordered two-dimensional Hubbard model with long-range interactions
Semiclassical dynamics of a disordered two-dimensional Hubbard model with long-range interactions
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具有长程相互作用的无序二维哈伯德模型的半经典动力学
DOI：
10.1103/physreva.102.033338
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发表时间：
2020
影响因子：
2.9
通讯作者：
Polkovnikov, Anatoli
中科院分区：
文献类型：
--
作者：
Sajna, Adam S.;Polkovnikov, Anatoli
用半经典截断维格纳近似（TWA）分析了二维费米子相互作用系统的猝灭动力学。考虑了具有近程和远距离相互作用的模型。我们证明在后一种情况下，TWA是非常精确的，在无限范围极限下变得渐近精确，只要正确地识别半经典哈密顿量。在TWA内，电荷和自旋的不同动态时标可以清晰地区分出来。有趣的是，对于弱和中等无序强度，我们观察到电荷的亚扩散行为，而自旋表现出扩散动力学。在强无序状态下，量子费雪信息随时间呈对数增长，电荷的增长比自旋的增长慢。结果表明，与短程模型相比，初始状态的强非均质性（如畴壁）可以显著减缓热化动力学，特别是在弱无序状态下。这种行为给设计旨在分析此类系统中可能的多体定位的冷原子实验方案带来了额外的挑战。虽然在这种方法中，我们不能对多体局域相的存在做出任何明确的声明，但我们看到，在短程和远程模型中，作为无序强度的函数，从快速热化到缓慢的玻璃状状态，都有一个非常快的交叉。
Quench dynamics in a two-dimensional system of interacting fermions is analyzed within the semiclassical truncated Wigner approximation (TWA). The models with short-range and long-range interactions are considered. We show that in the latter case, the TWA is very accurate, becoming asymptotically exact in the infinite-range limit, provided that the semiclassical Hamiltonian is correctly identified. Within the TWA, different dynamical timescales of charges and spins can be clearly distinguished. Interestingly, for a weak and moderate disorder strength, we observe subdiffusive behavior of charges, while spins exhibit diffusive dynamics. At strong disorder, the quantum Fisher information shows logarithmic growth in time with a slower increase for charges than for spins. It is shown that in contrast to the short-range model, strong inhomogeneities such as domain walls in the initial state can significantly slow down thermalization dynamics, especially at weak disorder. This behavior can put additional challenges in designing cold-atom experimental protocols aimed to analyze possible many-body localization in such systems. While within this approach we cannot make any definite statements about the existence of a many-body localized phase, we see a very fast crossover as a function of disorder strength from rapidly thermalizing to a slow glassylike regime both for the short-range and long-range models.
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