Fading ergodicity and quantum dynamics in random matrix ensembles

TL;DR

This paper demonstrates that the Rosenzweig-Porter and ultrametric random matrix models exhibit similar ergodicity-breaking behavior in many-body quantum systems, with local observables thermalizing faster than the Heisenberg time within the fading-ergodicity regime.

Contribution

It establishes a universality class for ergodicity breaking in these models and links their properties through quantum dynamics and observable statistics.

Findings

Local observables thermalize within the fading-ergodicity regime

Matrix elements of local observables show similar statistical properties

Fading ergodicity corresponds to the fractal phase in the models

Abstract

Recent work has proposed fading ergodicity as a mechanism for many-body ergodicity breaking. Here, we show that two paradigmatic random matrix ensembles -- the Rosenzweig-Porter model and the ultrametric model -- fall within the same universality class of ergodicity breaking when embedded in a many-body Hilbert space of spins-1/2. By calibrating the parameters of both models via their Thouless times, we demonstrate that the matrix elements of local observables display similar statistical properties, allowing us to identify the fractal phase of the Rosenzweig-Porter model with the fading-ergodicity regime. This correspondence is further supported through the analyses of quantum-quench dynamics of local observables, their temporal fluctuations and power spectra, and survival probabilities. Our findings reveal that local observables thermalize within the fading-ergodicity regime on timescales shorter than the Heisenberg time, thus providing a unified framework for understanding ergodicity breaking across these distinct models.