Ergodicity breaking transition in zero dimensions

TL;DR

This paper investigates a zero-dimensional quantum model to demonstrate an ergodicity breaking transition, confirming theoretical predictions through numerical spectral form factor analysis.

Contribution

It provides the first numerical confirmation of an ergodicity breaking transition in a zero-dimensional quantum model, linking it to the avalanche mechanism.

Findings

Spectral form factor matches theoretical predictions.

Confirmed ergodicity breaking transition in the model.

Identified properties characteristic of the transition.

Abstract

It is of great current interest to establish toy models of ergodicity breaking transitions in quantum many-body systems. Here we study a model that is expected to exhibit an ergodic to nonergodic transition in the thermodynamic limit upon tuning the coupling between an ergodic quantum dot and distant particles with spin-1/2. The model is effectively zero dimensional, however, a variant of the model was proposed by De Roeck and Huveneers to describe the avalanche mechanism of ergodicity breaking transition in one-dimensional disordered spin chains. We show that exact numerical results based on the spectral form factor calculation accurately agree with theoretical predictions, and hence unambiguously confirm existence of the ergodicity breaking transition in this model. We benchmark specific properties that represent hallmarks of the ergodicity breaking transition in finite systems.