Many-body localization as a $d = \infty$ Anderson localization with correlated disorder

TL;DR

This paper proposes that many-body localization (MBL) can be understood as an infinite-dimensional Anderson localization with correlated disorder, providing a new perspective on the fundamental nature of MBL.

Contribution

It introduces a novel interpretation of MBL as a $d=0$ Anderson localization with correlated disorder, linking the two phenomena through a virtual lattice model.

Findings

MBL can be modeled as an infinite-dimensional Anderson localization.

The critical disorder strength saturates in the thermodynamic limit.

Universal behavior is observed in entanglement entropy and energy level statistics.

Abstract

The disordered many-body systems can undergo a transition from the extended ensemble to a localized ensemble, known as many-body localization (MBL), which has been intensively explored in recent years. Nevertheless, the relation between Anderson localization (AL) and MBL is still elusive. Here we show that the MBL can be regarded as an infinite-dimensional AL with the correlated disorder in a virtual lattice. We demonstrate this idea using the disordered XXZ model, in which the excitation of $d$ spins over the fully polarized phase can be regarded as a single-particle model in a $d$ dimensional virtual lattice. With the increasing of $d$, the system will quickly approach the MBL phase, in which the infinite-range correlated disorder ensures the saturation of the critical disorder strength in the thermodynamic limit. From the transition from AL to MBL, the entanglement entropy and the critical exponent from energy level statics are shown to depend weakly on the dimension, indicating that belonging to the same universal class. This work clarifies the fundamental concept of MBL and presents a new picture for understanding the MBL phase in terms of AL.