Many-body localization and the area law in two dimensions

TL;DR

This study investigates many-body localization in a 2D spin system, demonstrating an area law for entanglement entropy in the localized phase and identifying a transition point to ergodicity using large-scale tensor network simulations.

Contribution

It provides the first large-scale numerical evidence of many-body localization with an area law in two dimensions, including an estimate of the transition point.

Findings

Existence of a many-body localized phase in 2D.

Localized states follow an area law for entanglement entropy.

Transition point to ergodic behavior identified in quenched disorder.

Abstract

We study the high-energy phase diagram of a two-dimensional spin-$\frac{1}{2}$ Heisenberg model on a square lattice in the presence of either quenched or quasiperiodic disorder. The use of large-scale tensor network numerics allows us to compute the bipartite entanglement entropy for systems of up to $60 \times 7$ lattice sites. We provide evidence for the existence of a many-body localized regime for large disorder strength that features an area law in excited states and that violates the eigenstate thermalization hypothesis. From a finite-size analysis, we determine an estimate for the critical disorder strength where the transition to the ergodic regime occurs in the quenched case.