无无序势中二维哈伯德模型的慢半经典动力学
Slow semiclassical dynamics of a two-dimensional Hubbard model in disorder-free potentials
摘要：
本文在半经典图象下讨论了倾斜势和谐振势中哈伯德模型的猝灭动力学。应用费米子截断Wigner近似（fTWA），分析了电荷和自旋自由度不平衡的动力学过程，并与一维晶格中的精确模拟结果进行了比较.考虑了电荷或自旋密度波的猝灭。我们表明，谐波和自旋相关的线性势的引入充分验证fTWA较长的时间。对于电荷和自旋通道的量子费舍尔信息的高阶关联，也获得了fTWA的这种改善。这使我们能够讨论更大系统尺寸的动力学，并将我们的讨论与最近引入的斯塔克多体局域化联系起来。特别是，我们专注于一个有限的二维系统，并表明，在中间的线性势强度，除了一个谐波势和自旋依赖的倾斜，结果在次扩散动力学，类似的无序系统。此外，对于特定值的谐波势，我们观察到的遍历和非遍历区域在实空间中的相位分离。后一个事实是特别重要的超冷原子实验中，谐波限制可以很容易地施加，导致不同的晶格位置的弛豫时间的显着变化。
英文摘要：
The quench dynamics of the Hubbard model in tilted and harmonic potentials is discussed within the semiclassical picture. Applying the fermionic truncated Wigner approximation (fTWA), the dynamics of imbalances for charge and spin degrees of freedom is analyzed and its time evolution is compared with the exact simulations in one-dimensional lattice. Quench from charge or spin density wave is considered. We show that introduction of harmonic and spin-dependent linear potentials sufficiently validates fTWA for longer times. Such an improvement of fTWA is also obtained for the higher order correlations in terms of quantum Fisher information for charge and spin channels. This allows us to discuss the dynamics of larger system sizes and connect our discussion to the recently introduced Stark many-body localization. In particular, we focus on a finite two-dimensional system and show that at intermediate linear potential strength, the addition of a harmonic potential and spin dependence of the tilt, results in subdiffusive dynamics, similar to that of disordered systems. Moreover, for specific values of harmonic potential, we observed phase separation of ergodic and non-ergodic regions in real space. The latter fact is especially important for ultracold atom experiments in which harmonic confinement can be easily imposed, causing a significant change in relaxation times for different lattice locations.
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