论文标题
特征态在跨离地化 - 位置相变的边界条件方面的鲁棒性和独立性
Robustness and Independence of the Eigenstates with respect to the Boundary Conditions across a Delocalization-Localization Phase Transition
论文作者
论文摘要
我们专注于跨定位 - 偏置相变的多体征本态。为了表征特征状态的鲁棒性，我们引入了特征态重叠$ \ MATHCAL {O} $相对于不同的边界条件。在ergodic阶段，特征态的平均值重叠$ \ bar {\ mathcal {o}} $是指数级的衰减，系统尺寸的增加表明其特征性属性的脆弱性，并且可以将其视为chaotic Systems的特征态性蝴蝶效应。对于本地化系统，$ \ bar {\ Mathcal {o}} $几乎是与大小无关的，显示了特征状态的强鲁棒性和特征态热假设的破裂。此外，我们发现特征态对多体局部系统中边界条件变化的响应与安德森局部系统中的单粒子波函数鉴定在一起。这表明，由于多体波函数，多体局部系统的本征态可能彼此独立。我们证明，这与多体局部阶段中大量运动积分的存在是一致的。我们的结果提供了一种新的方法，可以从本征态的角度研究局部和离域系统。
We focus on the many-body eigenstates across a localization-delocalization phase transition. To characterize the robustness of the eigenstates, we introduce the eigenstate overlaps $\mathcal{O}$ with respect to the different boundary conditions. In the ergodic phase, the average of eigenstate overlaps $\bar{\mathcal{O}}$ is exponential decay with the increase of the system size indicating the fragility of its eigenstates, and this can be considered as an eigenstate-version butterfly effect of the chaotic systems. For localized systems, $\bar{\mathcal{O}}$ is almost size-independent showing the strong robustness of the eigenstates and the broken of eigenstate thermalization hypothesis. In addition, we find that the response of eigenstates to the change of boundary conditions in many-body localized systems is identified with the single-particle wave functions in Anderson localized systems. This indicates that the eigenstates of the many-body localized systems, as the many-body wave functions, may be independent of each other. We demonstrate that this is consistent with the existence of a large number of quasilocal integrals of motion in the many-body localized phase. Our results provide a new method to study localized and delocalized systems from the perspective of eigenstates.
