论文标题
希尔伯特空间中的多体定位过渡
The Many-Body localization transition in the Hilbert space
论文作者
论文摘要
在本文中，我们提出了一种新的观点，以分析当在多体构型的空间中根据单粒子紧密结合模型进行重铸时，分析多体定位（MBL）过渡。我们计算多体状态之间的隧道速率分布，这些状态在扰动理论中以最低的顺序从绝缘体开始，并确定其典型幅度的缩放，并确定希尔伯特空间中可访问状态的数量。通过使用与Rosenzweig-Porter随机矩阵集合的类比，我们提出了基于Fermi Golden规则的MBL过渡的奇异性破坏标准。根据该标准，在MBL相中，许多共振在与无限温度初始状态的较大距离处形成，但是它们不足以使量子动力学在有限的时间内向其脱发。这意味着，与安德森本地化状态不同，在绝缘阶段，多体征本素质在希尔伯特空间中是多重分子的，因为它们占据了总数的较大但次指数的一部分，这与最近的数值结果，扰动计算和直觉的参数一致。在结论中讨论了我们解释的可能局限性和含义。
In this paper we propose a new perspective to analyze the many-body localization (MBL) transition when recast in terms of a single-particle tight-binding model in the space of many-body configurations. We compute the distribution of tunneling rates between many-body states separated by an extensive number of spin flips at the lowest order in perturbation theory starting from the insulator, and determine the scaling of their typical amplitude with the number of accessible states in the Hilbert space. By using an analogy with the Rosenzweig-Porter random matrix ensemble, we propose an ergodicity breaking criterion for the MBL transition based on the Fermi Golden Rule. According to this criterion, in the MBL phase many resonances are formed at large distance from an infinite temperature initial state, but they are not enough for the quantum dynamics to decorrelate from it in a finite time. This implies that, differently from Anderson localized states, in the insulating phase many-body eigenstates are multifractal in the Hilbert space, as they occupy a large but subexponential part of the total volume, in agreement with recent numerical results, perturbative calculations, and intuitive arguments. Possible limitations and implications of our interpretation are discussed in the conclusions.
