A semi-classical limit for the many-body localization transition

TL;DR

This paper introduces a semi-classical limit using Clifford circuits to study many-body localization, revealing stable localized and delocalized phases and a continuous transition in higher dimensions, providing insights into critical behavior.

Contribution

It presents a new semi-classical Clifford circuit model for many-body localization, analyzing phase stability and transition properties across different dimensions.

Findings

In 1D, the system is always many-body localized with local integrals of motion.

In higher dimensions, the model exhibits both localized and delocalized phases separated by a continuous transition.

The model suggests bounds on critical exponents for the generic many-body localization transition.

Abstract

We introduce a semi-classical limit for many-body localization in the absence of global symmetries. Microscopically, this limit is realized by disordered Floquet circuits composed of Clifford gates. In $d=1$, the resulting dynamics are always many-body localized with a complete set of strictly local integrals of motion. In $d\geq 2$, the system realizes both localized and delocalized phases separated by a continuous transition in which ergodic puddles percolate. We argue that the phases are stable to deformations away from the semi-classical limit and estimate the resulting phase boundary. The Clifford circuit model is a distinct tractable limit from that of free fermions and suggests bounds on the critical exponents for the generic transition.