Scaling theory of fading ergodicity

TL;DR

This paper introduces a two-parameter scaling theory for fading ergodicity in quantum systems, bridging the gap between ergodic and many-body localized regimes, and predicting critical behavior at the ergodicity breaking transition.

Contribution

It proposes a novel two-parameter scaling framework for fading ergodicity, extending the understanding of ergodic to non-ergodic transitions in many-body quantum systems.

Findings

Two-parameter scaling governs the entire ergodic regime.

At the critical point, it reduces to one-parameter scaling with exponent ν=1.

Near the ETH point, it predicts resilient one-parameter scaling.

Abstract

In most noninteracting quantum systems, the scaling theory of localization predicts one-parameter scaling flow in both ergodic and localized regimes. On the other hand, it is expected that the one-parameter scaling hypothesis breaks down for interacting systems that exhibit the many-body ergodicity breaking transition. Here we introduce a scaling theory of fading ergodicity, which is a precursor regime of many-body ergodicity breaking. We argue that the two-parameter scaling governs the entire ergodic regime; however, (i) it evolves into the one-parameter scaling at the ergodicity breaking critical point with the critical exponent $\nu=1$, and (ii) it gives rise to the resilient one-parameter scaling close to the ETH point. Our theoretical framework may serve as a building block for two-parameter scaling theories of many-body systems.