Roughening and dynamics of an electric flux string in a (2+1)D lattice gauge theory

TL;DR

This paper studies the roughening transition of electric flux strings in a (2+1)D $ ext{Z}_2$ lattice gauge theory, revealing universal corrections, symmetry restoration, and distinct entanglement dynamics across phases.

Contribution

It provides the first numerical analysis of the roughening transition in a (2+1)D lattice gauge theory using matrix product states, highlighting universal effects and out-of-equilibrium behavior.

Findings

Universal Lüscher correction observed in the roughening phase

Restoration of rotational symmetry near the transition

Distinct entanglement growth behavior in different phases

Abstract

We investigate the roughening transition in the pure $\mathbb{Z}_2$ lattice gauge theory in (2+1) dimensions. Using numerical simulations with matrix product states, we explore the static and dynamical properties of an electric flux string between two static charges as the coupling is varied and approaches the deconfinement phase transition from the confined phase. Within the roughening region, we obtain the universal L\"uscher correction to the confining potential and observe the expected restoration of rotational symmetry. Our simulations of the out-of-equilibrium evolution of a string reveal that the growth of the entanglement entropy of the state and the string width exhibit qualitatively different behavior in the roughening region compared to the deeply confined one. In particular, we find that the rate of entropy growth is consistent with an effective description of the string excitations by a bosonic model in the roughening phase.