Many-body localization as a percolation phenomenon

TL;DR

This paper models many-body localization as a percolation problem in Fock space, revealing how eigenstates form disconnected clusters at strong disorder and capturing transport phenomena including subdiffusive behavior.

Contribution

It introduces a percolation-based framework for analyzing MBL, simplifying the quantum problem to rate equations and identifying the transition via cluster distributions.

Findings

MBL corresponds to disconnected clusters in Fock space at strong disorder

The rate equation approach captures diffusion and subdiffusive transport

The transition is characterized by the emergence of a macroscopic cluster

Abstract

We examine the standard model of many-body localization (MBL), i.e., the disordered chain of interacting spinless fermions, by representing it as the network in the many-body (MB) basis of noninteracting localized Anderson states. By studying eigenstates of the full Hamiltonian, for strong disorders we find that the dynamics is confined up to very long times to disconnected MB clusters in the Fock space. By keeping only resonant contributions and simplifying the quantum problem to rate equations (REs) for MB states, in analogy with percolation problems, the MBL transition is located via the universal cluster distribution and the emergence of the macroscopic cluster. On the ergodic side, our approximate RE approach to the relaxation processes captures well the diffusion transport, as found for the full quantum model. In a broad transient regime, we find an anomalous, i.e., subdiffusivelike, transport, emerging from weak links between MB states.