Scaling Theory of Fading Ergodicity

In most noninteracting quantum systems, the scaling theory of localization predicts one-parameter scaling flow in both ergodic and localized regimes. A corresponding scaling theory of many-body ergodicity breaking is still missing. Here, we introduce a scaling theory of ergodicity breaking in interacting systems, in which the divergent relaxation time follows from the Fermi golden rule, and the observable fluctuations in proximity of the ergodicity breaking critical point are described by the recently introduced fading ergodicity scenario. We argue that, in general, the one-parameter scaling is insufficient, and we show that the scaling theory predicts the critical exponent ν=1 at the ergodicity breaking critical point. Our theoretical framework may serve as a building block for two-parameter scaling theories of many-body systems.