Towards absolutely stable ergodicity breaking in two and three dimensions

TL;DR

This paper introduces new physical systems in two and three dimensions that exhibit stable ergodicity breaking at infinite time, even under generic perturbations and thermal coupling, by leveraging emergent symmetries and topological features.

Contribution

The authors construct models with exponentially many nonergodic states that remain stable in the thermodynamic limit, extending ergodicity-breaking phenomena to more realistic settings.

Findings

In 2D, exponentially many stable nonergodic states with diverging energy but zero energy density.

In 3D, exponentially many states with diverging energy barriers leading to robust ergodicity breaking.

The models connect to quantum dimer models, topological order, and anomalous entanglement entropy.

Abstract

We propose new physically reasonable systems capable of avoiding ergodicity at infinite time in the thermodynamic limit, even with generic perturbations and when coupled to a heat bath. In two dimensions, the rainbow loop soup has (stretched) exponentially numerous absolutely stable nonergodic states with diverging energy but vanishing energy density. In three dimensions the rainbow membrane soup has (stretched) exponentially numerous nonergodic states with diverging energy barriers, leading to infinite-time robust ergodicity breaking that even survives coupling to a nonzero temperature heat bath. We describe our results in the language of exact emergent symmetries and demonstrate how the systems avoid common instabilities. Our construction naturally connects to quantum dimer models, topologically ordered systems, the group word construction, and Hamiltonians whose low-energy eigenstates exhibit anomalous entanglement entropy.