Topologically stable ergodicity breaking from emergent higher-form symmetries in generalized quantum loop models

TL;DR

This paper introduces generalized quantum loop models with emergent higher-form symmetries that cause topologically stable ergodicity breaking, applicable under various boundary conditions and linked to dualities with existing models.

Contribution

It demonstrates the existence of models with emergent one-form symmetry leading to ergodicity breaking as a prethermal phenomenon, expanding understanding of symmetry-protected non-ergodic phases.

Findings

Models exhibit topologically stable ergodicity breaking.

Emergent one-form symmetry causes long-lived prethermal states.

Robust nonlocal conserved quantities linked to system-spanning domain walls.

Abstract

We present a set of generalized quantum loop models which provably exhibit topologically stable ergodicity breaking. These results hold for both periodic and open boundary conditions, and derive from a one-form symmetry (notably not being restricted to sectors of extremal one-form charge). We identify simple models in which this one-form symmetry can be emergent, giving rise to the aforementioned ergodicity breaking as an exponentially long-lived prethermal phenomenon. We unveil a web of dualities that connects these models, in certain limits, to models that have previously been discussed in the literature. We also identify nonlocal conserved quantities in such models that correspond to a pattern of system-spanning domain walls, and which are robust to the addition of arbitrary $k$-local perturbations.