Ergodicity breaking in a model showing many-body localization

TL;DR

This paper investigates ergodicity breaking in a quantum spin chain, identifying many-body localization through wave function distribution analysis and proposing a robust criterion for the transition.

Contribution

It introduces a new criterion based on wave function coefficient distributions to identify many-body localization transitions in quantum systems.

Findings

Ergodicity is broken in the studied quantum spin chain.

Participation ratios scale anomalously with system size.

A robust criterion for many-body localization transition is proposed.

Abstract

We study the breaking of ergodicity measured in terms of return probability in the evolution of a quantum state of a spin chain. In the non ergodic phase a quantum state evolves in a much smaller fraction of the Hilbert space than would be allowed by the conservation of extensive observables. By the anomalous scaling of the participation ratios with system size we are led to consider the distribution of the wave function coefficients, a standard observable in modern studies of Anderson localization. We finally present a criterion for the identification of the ergodicity breaking (many-body localization) transition based on these distributions which is quite robust and well suited for numerical investigations of a broad class of problems.