无序系统弛豫机制的Poisson能级统计
Relaxation mechanisms in a disordered system with the Poisson level statistics
摘要：
我们讨论了多体局域化和自旋对称性之间的相互作用。为此，我们研究了各向异性t-J模型中几个观测量的时间演化。像哈伯德链一样，研究的模型包含电荷和自旋自由度，但它具有较小的希尔伯特空间，因此可以对更大的系统进行数值研究。我们比较了打破Z_2自旋对称性的场无序和保持后者对称性的势无序。在前一种情况下，足够强的混乱导致本地化的所有研究的可观的，至少对于所研究的系统的大小。然而，在保序无序的情况下，我们观察到奇算符在Z_2自旋变换下在相对较短的时间尺度上向平衡值弛豫，并且仅随无序强度的多项式增长。另一方面，偶算子的动力学和每个对称扇区内的水平统计与局部化是一致的。我们的研究结果表明，本地化存在于每个对称性部门的对称性保持无序。奇算子的表观弛豫是由于它们在不同对称扇区之间的时间演化。
英文摘要：
We discuss the interplay between many-body localization and spin-symmetry. To this end, we study the time evolution of several observables in the anisotropic t-J model. Like the Hubbard chain, the studied model contains charge and spin degrees of freedom, yet it has smaller Hilbert space and thus allows for numerical studies of larger systems. We compare the field disorder that breaks the Z_2 spin symmetry and a potential disorder that preserves the latter symmetry. In the former case, sufficiently strong disorder leads to localization of all studied observables, at least for the studied system sizes. However, in the case of symmetry-preserving disorder, we observe that odd operators under the Z_2 spin transformation relax towards the equilibrium value at relatively short time scales that grow only polynomially with the disorder strength. On the other hand, the dynamics of even operators and the level statistics within each symmetry sector are consistent with localization. Our results indicate that localization exists within each symmetry sector for symmetry preserving disorder. Odd operators' apparent relaxation is due to their time evolution between distinct symmetry sectors.
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