Many-Body Localization in Two Dimensions from Projected Entangled-Pair States

TL;DR

This paper investigates many-body localization in two-dimensional lattice systems using PEPS, comparing different disorder types and establishing localization markers through information loss rate, entanglement, and participation ratio.

Contribution

It introduces a PEPS-based method to analyze 2D localization, comparing disorder types and identifying markers for localization in interacting systems.

Findings

Disorder strength for localization increases with system dimensionality and interaction.

Cases (i) and (ii) show similar localization behavior, case (iii) requires stronger disorder.

Information loss rate effectively indicates localization transition.

Abstract

Using projected entangled-pair states (PEPS) we analyze the localization properties of two-dimensional systems on a square lattice. We compare the dynamics found for three different disorder types: (i) quenched disorder, (ii) sum of two quasi-periodic potentials along both spatial dimensions and (iii) a single quasi-periodic potential rotated with respect to the underlying lattice by a given angle. We establish the rate of loss of information, a quantity measuring the error made while simulating the dynamics, as a good hallmark of localization physics by comparing to entanglement build-up as well as the inverse participation ratio in exactly solvable limits. We find that the disorder strength needed to localize the system increases both with the dimensionality of as well as the interaction strength in the system. The first two cases of potential (i) and (ii) behave similar, while case (iii) requires larger disorder strength to localize.