Identifying quantum many-body integrability and chaos using eigenstates trace distances

TL;DR

This paper introduces a new eigenstate-based indicator using trace distances to distinguish quantum many-body integrability from chaos, providing a more faithful classification across various models and overcoming limitations of traditional level-spacing methods.

Contribution

The authors propose a novel eigenstate trace distance measure for identifying quantum many-body integrability and chaos, validated through extensive numerical simulations on diverse models.

Findings

The indicator accurately classifies integrability and chaos in various models.

It outperforms traditional level-spacing statistics in certain regimes.

Universal behaviors of trace distances are observed across different systems.

Abstract

While the concepts of quantum many-body integrability and chaos are of fundamental importance for the understanding of quantum matter, their precise definition has so far remained an open question. In this work, we introduce an alternative indicator for quantum many-body integrability and chaos, which is based on the statistics of eigenstates by means of nearest-neighbor subsystem trace distances. We show that this provides us with a faithful classification through extensive numerical simulations for a large variety of paradigmatic model systems including random matrix theories, free fermions, Bethe-ansatz solvable systems, and models of many-body localization. While existing indicators, such as those obtained from level-spacing statistics, have already been utilized with great success, they also face limitations. This concerns for instance the quantum many-body kicked top, which is exactly solvable but classified as chaotic in certain regimes based on the level-spacing statistics, while our introduced indicator signals the expected quantum many-body integrability. We discuss the universal behaviors we observe for the nearest-neighbor trace distances and point out that our indicator might be useful also in other contexts such as for the many-body localization transition.