Fading ergodicity meets maximal chaos

TL;DR

This paper explores how fading ergodicity explains deviations from ETH near ergodicity-breaking transitions, revealing maximal chaos and divergent fidelity susceptibilities in quantum models.

Contribution

It demonstrates the link between fading ergodicity and maximal chaos, extending analysis to energy-driven transitions and fidelity susceptibility behavior.

Findings

ETH breakdown at ergodicity-breaking critical point causes maximal divergence in fidelity susceptibility.

Fidelity susceptibilities peak near the mobility edge away from the spectrum center.

Fading ergodicity accurately describes ETH breakdown and chaos emergence in the quantum sun model.

Abstract

Fading ergodicity provides a theoretical framework for understanding deviations from the eigenstate thermalization hypothesis (ETH) near ergodicity-breaking transitions. In this work, we demonstrate that the breakdown of the ETH at the interaction-driven ergodicity-breaking critical point in the quantum sun model gives rise to to the maximally divergent fidelity susceptibility. We further extend our analysis to the energy-driven ergodicity-breaking transition associated with the many-body mobility edge. Specifically, we show that fidelity susceptibilities at energies away from the middle of the spectrum exhibit a divergent peak near the mobility edge. Finally, we argue that fading ergodicity provides a simple and accurate description of the ETH breakdown in the quantum sun model, which is accompanied with the emergence of a peak in fidelity susceptibility and the onset of maximal chaos at the ergodicity-breaking critical point.