Total correlations of the diagonal ensemble as a generic indicator for ergodicity breaking in quantum systems

TL;DR

This paper introduces total correlations of the diagonal ensemble as a universal indicator of ergodicity breaking in quantum systems, linking quantum information measures to quantum ergodic properties.

Contribution

It generalizes total correlations to Renyi entropies and demonstrates their effectiveness in detecting ergodicity breaking and many-body localization transitions.

Findings

Total correlations scale sub-extensively in ergodic systems.

Total correlations indicate ergodicity breaking in spin chains.

The measure helps understand transitions to many-body localized phases.

Abstract

The diagonal ensemble is the infinite time average of a quantum state following unitary dynamics. In analogy to the time average of a classical phase space dynamics, it is intimately related to the ergodic properties of the quantum system giving information on the spreading of the initial state in the eigenstates of the Hamiltonian. In this work we apply a concept from quantum information, known as total correlations, to the diagonal ensemble. Forming an upper-bound on the multipartite entanglement, it quantifies the combination of both classical and quantum correlations in a mixed state. We generalize the total correlations of the diagonal ensemble to more general $\alpha$-Renyi entropies and focus on the the cases $\alpha=1$ and $\alpha=2$ with further numerical extensions in mind. Here we show that the total correlations of the diagonal ensemble is a generic indicator of ergodicity breaking, displaying a sub-extensive behaviour when the system is ergodic. We demonstrate this by investigating its scaling in a range of spin chain models focusing not only on the cases of integrability breaking but also emphasize its role in understanding the transition from an ergodic to a many body localized phase in systems with disorder or quasi-periodicity.