Non-ergodic delocalized phase with Poisson level statistics

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 nonergodic 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. 4 Analytical consideration 13 5 Conclusion and outlook 18 References 19 A Coherent potential approximation 23