An Explicit Bound for Dynamical Localisation in an Interacting Many-Body System

TL;DR

This paper provides explicit bounds on the disorder strength needed for dynamical localisation in an interacting quantum many-body system, using novel mathematical techniques applicable beyond the specific model studied.

Contribution

It introduces a new fractional moment criterion and path-sums method to establish localisation bounds in many-body quantum systems, generalizable to broader settings.

Findings

Explicit disorder bounds for localisation in the XYZ model

Bounds on magnetisation and magnetic response in the localised regime

Numerical confirmation of theoretical results

Abstract

We characterise and study dynamical localisation of a finite interacting quantum many-body system. We present explicit bounds on the disorder strength required for the onset of localisation of the dynamics of arbitrary ensemble of sites of the XYZ spin-1/2 model. We obtain these results using a novel form of the fractional moment criterion, which we establish, together with a generalisation of the self-avoiding walk representation of the system Green's functions, called path-sums. These techniques are not specific to the XYZ model and hold in a much more general setting. We further present bounds for two observable quantities in the localised regime: the magnetisation of any sublattice of the system as well as the linear magnetic response function of the system. We confirm our results through numerical simulations.