Disorder-Free Localization as a Purely Classical Effect

TL;DR

This paper demonstrates that disorder-free localization (DFL) in lattice gauge theories can occur as a purely classical effect, not solely due to quantum interference, by modeling with cellular automaton circuits.

Contribution

It shows that DFL persists in the thermodynamic limit as a classical phenomenon arising from finite-size regularization in quantum link models.

Findings

DFL occurs as a classical effect in large systems.

Cellular automaton models agree with quantum results for small sizes.

Quantum interference can enhance but is not necessary for DFL.

Abstract

Disorder-free localization (DFL) is an ergodicity breaking mechanism that has been shown to occur in lattice gauge theories in the quench dynamics of initial states spanning an extensive number of gauge superselection sectors. Whether DFL is intrinsically a quantum interference effect or can arise classically has hitherto remained an open question whose resolution is pertinent to further understanding the far-from-equilibrium dynamics of gauge theories. In this work, we utilize cellular automaton circuits to model the quench dynamics of large-scale quantum link model (QLM) formulations of $(1+1)$D quantum electrodynamics, showing excellent agreement with the exact quantum case for small system sizes. Our results demonstrate that DFL persists in the thermodynamic limit as a purely classical effect arising from the finite-size regularization of the gauge-field operator in the QLM formulation, and that quantum interference, though not a necessary condition, may be employed to enhance DFL.