Topological glass states

TL;DR

This paper explores classical lattice spin models that exhibit topological glass states, characterized by topologically distinct low-energy configurations that break ergodicity without breaking symmetry, expanding understanding of topological phases beyond quantum systems.

Contribution

It introduces and analyzes classical models demonstrating topological glass states, highlighting their unique ergodicity-breaking properties without symmetry breaking.

Findings

Topological glass states can occur in classical lattice spin models.

These states are characterized by topologically distinct low-energy configurations.

The models show ergodicity breaking without symmetry breaking.

Abstract

In connection with recent discussion of topological order and topological phase transitions in quantum systems, we reexamine circumstances that lead to the appearance of a topological glass in certain classical lattice spin models. Local bonding enforces constraints on low energy states which organize themselves into topologically distinct classes that break ergodicity but not any apparent symmetry as in the usual Landau theory of phase transitions. Various properties of such a topological glass are demonstrated using two classical Ising-like models.