从遍历性到一维相互作用非厄米斯塔克系统中的多体局域化
From Ergodicity to Many-Body Localization in a One-Dimensional Interacting Non-Hermitian Stark System
AI总结：
本文研究了一维相互作用非厄米Stark模型，发现在周期边界条件下存在实复转变、拓扑相变和非厄米Stark多体局域化（MBL）转变，并通过能级统计和动力学演化揭示了这些相变特征。
摘要：
近期关于非厄米量子系统中无序诱导的多体局域化（MBL）的研究引起了极大兴趣。然而，无无序的非厄米MBL仍需进一步阐明。我们考虑一个具有时间反演对称性且包含非互易跃迁的一维相互作用Stark模型，其性质依赖于边界条件。在周期边界条件（PBCs）下，该模型表现出三类相变：本征能量的实复转变、拓扑相变以及非厄米Stark MBL转变。在热力学极限下，实复转变与拓扑相变发生在同一点，但与非厄米Stark MBL转变并不重合，这与非厄米无序情况截然不同。通过能级统计，随着线性倾斜势强度的增加，系统从Ginibre系综（GE）转变为高斯正交系综（GOE），再转变为泊松系综。本征值的实复转变伴随着遍历区中的GE到GOE转变。此外，能级统计的第二次转变对应着非厄米Stark MBL的出现。我们证明非厄米Stark MBL具有鲁棒性，并与无序诱导的MBL具有许多相似之处，这可由谱统计和本征态性质的几个现有特征量来证实。纠缠熵和密度不平衡的动力学演化可以区分实复转变和Stark MBL转变。最后，我们发现系统在开放边界条件下缺乏实复转变，且非厄米Stark MBL的转变与PBCs下的转变相同。
英文摘要：
Recent studies on disorder-induced many-body localization (MBL) in non-Hermitian quantum systems have attracted great interest. However, the non-Hermitian disorder-free MBL still needs to be clarified. We consider a one-dimensional interacting Stark model with nonreciprocal hoppings having time-reversal symmetry, the properties of which are boundary dependent. Under periodic boundary conditions (PBCs), such a model exhibits three types of phase transitions: the real-complex transition of eigenenergies, the topological phase transition, and the non-Hermitian Stark MBL transition. The real-complex and topological phase transitions occur at the same point in the thermodynamic limit but do not coincide with the non-Hermitian Stark MBL transition, which is quite different from the non-Hermitian disordered cases. By the level statistics, the system transitions from the Ginibre ensemble (GE) to the Gaussian orthogonal ensemble (GOE) to the Possion ensemble with the increase of the linear tilt potential's strength. The real-complex transition of the eigenvalues is accompanied by the GE-to-GOE transition in the ergodic regime. Moreover, the second transition of the level statistics corresponds to the occurrence of non-Hermitian Stark MBL. We demonstrate that the non-Hermitian Stark MBL is robust and shares many similarities with disorder-induced MBL, which several existing characteristic quantities of the spectral statistics and eigenstate properties can confirm. The dynamical evolutions of the entanglement entropy and the density imbalance can distinguish the real-complex and Stark MBL transitions. Finally, we find that our system under open boundary conditions lacks a real-complex transition, and the transition of non-Hermitian Stark MBL is the same as that under PBCs.
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