Disorder-Free Localization in $2+1$D Lattice Gauge Theories with Dynamical Matter

TL;DR

This paper demonstrates that disorder-free localization (DFL) persists in 2+1D lattice gauge theories with dynamical matter, with its strength influenced by initial matter configurations and propagation directionality, extending understanding beyond 1+1D systems.

Contribution

It shows that DFL survives in 2+1D lattice gauge theories with dynamical matter and identifies propagation directionality as a key factor affecting DFL strength.

Findings

DFL persists in 2+1D LGTs, though less pronounced than in 1+1D.

The initial matter configuration significantly influences DFL.

Propagation directionality of matter determines the strength of DFL.

Abstract

Disorder-free localization (DFL) has been established as a mechanism of strong ergodicity breaking in $1+1$D lattice gauge theories (LGTs) with dynamical matter for quenches starting in homogeneous initial states that span an extensive number of gauge superselection sectors. Nevertheless, the fate of DFL in $2+1$D in the presence of dynamical matter has hitherto remained an open question of great interest in light of the instability of quenched-disorder many-body localization in higher spatial dimensions. Using infinite matrix product state calculations, we show that DFL survives in $2+1$D LGTs, albeit it is generally less pronounced than in $1+1$D, and highly depends on the matter configuration of the initial state. Through suitable matter configurations, we are able to relate and compare the $1+1$D and $2+1$D cases, showing that the main ingredient for the strength of DFL in our setup is the \textit{propagation directionality} of matter. Our results suggest that, generically, DFL is weakened with increasing spatial dimension, although it can be made independent of the latter by minimizing the propagation directionality of matter in the initial state.