Scaling theory of fading ergodicity
arXiv:2412.15331 · doi:10.1103/4l42-l7pk
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 , 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.
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