Motivated by the many-body localization (MBL) phase in generic interacting disordered quantum systems, we develop a model simulating the same eigenstate structure like in MBL, but in the random-matrix setting. Demonstrating the absence of energy level repulsion (Poisson statistics), this model carries non-ergodic eigenstates, delocalized over the extensive number of configurations in the Hilbert space. On the above example, we formulate general conditions to a single-particle and random-matrix models in order to carry such states, based on the transparent generalization of the Anderson localization of single-particle states and multiple resonances.

中文翻译：

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具有泊松水平统计的非遍历离域阶段

受通用相互作用无序量子系统中的多体定位 (MBL) 阶段的启发，我们开发了一个模型来模拟与 MBL 中相同的本征态结构，但在随机矩阵设置中。证明不存在能级排斥（泊松统计），该模型带有非遍历本征态，在希尔伯特空间中的大量配置上离域。在上面的例子中，我们基于对单粒子状态和多重共振的安德森定位的透明概括，将一般条件公式化为单粒子和随机矩阵模型以承载这些状态。