Disorder-Free Localization and Fragmentation in a Non-Abelian Lattice Gauge Theory

TL;DR

This paper explores how non-Abelian gauge symmetries influence quantum many-body systems, revealing phases including ergodic, fragmented, and disorder-free localized states, with implications for quantum simulation.

Contribution

It maps the dynamical phase diagram of a (1+1)D SU(2) lattice gauge theory with matter, uncovering novel disorder-free localization phenomena due to non-Abelian symmetries.

Findings

Identified three distinct dynamical regimes: ergodic, fragmented nonthermal, and disorder-free localized.

Discovered that superpositions of gauge sectors can preserve inhomogeneities over time.

Highlighted potential for realizing these phases on qudit quantum processors.

Abstract

We investigate how isolated quantum many-body systems dynamically equilibrate under non-Abelian gauge-symmetry constraints. By encoding gauge superselection sectors into static $\mathrm{SU}(2)$ background charges, we map out the dynamical phase diagram of a (1+1)D $\mathrm{SU}(2)$ lattice gauge theory with dynamical matter. We uncover three distinct regimes: (i) an ergodic phase, (ii) a fragmented phase that is nonthermal but delocalized, and (iii) a disorder-free many-body localized regime. In the latter, a superposition of gauge superselection sectors preserves spatial matter inhomogeneities in time, as evidenced by distinct temporal scalings of entropy. We highlight the non-Abelian nature of these phases and argue for potential realizations on qudit processors.