# Dynamical Localization in $\mathbb{Z}_2$ Lattice Gauge Theories

## TL;DR

This paper investigates charge localization in two-dimensional $ ext{Z}_2$ lattice gauge theories after quantum quenches, revealing a disorder mechanism from gauge degrees of freedom and exploring localization, delocalization, and many-body effects.

## Contribution

It introduces a generic localization mechanism in $ ext{Z}_2$ gauge theories without quenched disorder, highlighting emergent binary disorder and its impact on localization and delocalization transitions.

## Key findings

- Charge localization occurs without quenched disorder due to conserved $ ext{Z}_2$ charges.
- Emergent binary disorder leads to unique localization behaviors and quantum percolation transitions.
- Interactions can induce many-body localization-like entanglement growth or transient localization.

## Abstract

We study quantum quenches in two-dimensional lattice gauge theories with fermions coupled to dynamical $\mathbb{Z}_2$ gauge fields. Through the identification of an extensive set of conserved quantities, we propose a generic mechanism of charge localization in the absence of quenched disorder both in the Hamiltonian and in the initial states. We provide diagnostics of this localization through a set of experimentally relevant dynamical measures, entanglement measures, as well as spectral properties of the model. One of the defining features of the models that we study is a binary nature of emergent disorder, related to $\mathbb{Z}_2$ degrees of freedom. This results in a qualitatively different behaviour in the strong disorder limit compared to typically studied models of localization. For example it gives rise to a possibility of a delocalization transition via a mechanism of quantum percolation in dimensions higher than 1D. We highlight the importance of our general phenomenology to questions related to dynamics of defects in Kitaev's toric code, and to quantum quenches in Hubbard models. While the simplest models we consider are effectively non-interacting, we also include interactions leading to many-body localization-like logarithmic entanglement growth. Finally, we consider effects of interactions that generate dynamics for conserved charges, which gives rise to only transient localization behaviour, or quasi-many-body-localization.