Universal properties of many-body delocalization transitions

TL;DR

This paper investigates the universal critical behavior of many-body delocalization transitions in one-dimensional systems, revealing a continuous phase transition with anomalous subdiffusive dynamics and diverging critical exponents.

Contribution

The authors develop an effective model incorporating collective resonant tunneling to analytically and numerically characterize the universal properties of many-body delocalization transitions.

Findings

Identification of a continuous dynamical phase transition from many-body localized to thermal states.

Discovery of a broad subdiffusive regime with a diverging dynamical critical exponent.

Derivation of the universal scaling structure connecting microscopic physics to critical phenomena.

Abstract

We study the dynamical melting of "hot" one-dimensional many-body localized systems. As disorder is weakened below a critical value these non-thermal quantum glasses melt via a continuous dynamical phase transition into classical thermal liquids. By accounting for collective resonant tunneling processes, we derive and numerically solve an effective model for such quantum-to-classical transitions and compute their universal critical properties. Notably, the classical thermal liquid exhibits a broad regime of anomalously slow sub-diffusive equilibration dynamics and energy transport. The subdiffusive regime is characterized by a continuously evolving dynamical critical exponent that diverges with a universal power at the transition. Our approach elucidates the universal long-distance, low-energy scaling structure of many-body delocalization transitions in one dimension, in a way that is transparently connected to the underlying microscopic physics.