Effective field theory approach to many-body localization

TL;DR

This paper develops an analytic field theory approach to understand many-body localization in random spin chains, viewing MBL as a localization phenomenon in the high-dimensional Hilbert space.

Contribution

It introduces a novel first quantized field theory framework to analyze the stability of different disorder phases in many-body localized systems.

Findings

Field theory distinguishes between weak and strong disorder phases.

The approach provides insights into the stability of MBL phases.

Analytic tools for studying phase transitions in disordered quantum systems.

Abstract

We construct an analytic theory of many-body localization (MBL) in random spin chains. The approach is based on a first quantized perspective in which MBL is understood as a localization phenomenon on the high dimensional lattice defined by the discrete Hilbert space of the clean system. We construct a field theory on that lattice and apply it to discuss the stability of a weak disorder (`Wigner-Dyson') and a strong disorder (`Poisson') phase.