Disorder-free localization transition in a two-dimensional lattice gauge theory

TL;DR

This paper characterizes the disorder-free quantum localization transition in a 2D lattice gauge theory, linking it to a classical percolation transition and analyzing its critical behavior.

Contribution

It provides the first comprehensive analysis of the quantum localization transition in 2D disorder-free lattice gauge theories, connecting it to percolation theory.

Findings

Identification of two regimes: non-ergodic large clusters and ergodic large clusters.

Demonstration that the localization transition is continuous and equivalent to a classical percolation transition.

Finite-size scaling analysis revealing the universality class of the transition.

Abstract

Disorder-free localization is a novel mechanism for ergodicity breaking which can occur in interacting quantum many-body systems such as lattice gauge theories (LGTs). While the nature of the quantum localization transition (QLT) is still debated for conventional many-body localization, here we provide the first comprehensive characterization of the QLT in two dimensions (2D) for a disorder-free case. Disorder-free localization can appear in homogeneous 2D LGTs such as the U(1) quantum link model (QLM) due to an underlying classical percolation transition fragmenting the system into disconnected real-space clusters. Building on the percolation model, we characterize the QLT in the U(1) QLM through a detailed study of the ergodicity properties of finite-size real-space clusters via level-spacing statistics and localization in configuration space. We argue for the presence of two regimes - one in which large finite-size clusters effectively behave non-ergodically, a result naturally accounted for as an interference phenomenon in configuration space and the other in which all large clusters behave ergodically. As one central result, in the latter regime we claim that the QLT is equivalent to the classical percolation transition and is hence continuous. Utilizing this equivalence we determine the universality class and critical behaviour of the QLT from a finite-size scaling analysis of the percolation problem.