Non-ergodic delocalized phase with Poisson level statistics

TL;DR

This paper introduces a random-matrix model that mimics many-body localization features, exhibiting non-ergodic, delocalized eigenstates with Poisson level statistics, expanding understanding of non-ergodic phases in disordered quantum systems.

Contribution

The paper develops a novel random-matrix model capturing non-ergodic, delocalized eigenstates similar to MBL, with general conditions for such states based on Anderson localization and resonances.

Findings

Model exhibits Poisson level statistics and non-ergodic eigenstates.

Provides conditions for non-ergodic delocalized states in single-particle and random-matrix models.

Connects Anderson localization concepts to many-body localization phenomena.

Abstract

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.