Classical height models with topological order

TL;DR

This paper explores a class of statistical-mechanics models with group-valued edge elements on lattices, exhibiting topological order, including non-abelian cases, and discusses criteria for model viability and Monte Carlo updates.

Contribution

It introduces a family of height models with topological order based on finite groups, including non-abelian groups, and provides criteria for their viability and simulation methods.

Findings

Models can exhibit non-abelian topological order.

Criteria for model viability and Monte Carlo updates are established.

The models extend classical height models with new topological properties.

Abstract

I discuss a family of statistical-mechanics models in which (some classes of) elements of a finite group $G$ occupy the (directed) edges of a lattice; the product around any plaquette is constrained to be the group identity $e$. Such a model may possess topological order, i.e. its equilibrium ensemble has distinct, symmetry-related thermodynamic components that cannot be distinguished by any local order parameter. In particular, if $G$ is a non-abelian group, the topological order may be non-abelian. Criteria are given for the viability of particular models, in particular for Monte Carlo updates.