Phase transitions in three-dimensional topological lattice models with surface anyons

TL;DR

This paper investigates phase transitions in 3D Walker-Wang lattice models, revealing how surface anyons and bulk deconfinement are affected by perturbations, with phase diagrams analogous to generalized Z_p gauge theories.

Contribution

It demonstrates the exact correspondence between Walker-Wang phase transitions and generalized Z_p lattice gauge theories, highlighting unique bulk deconfinement phenomena.

Findings

Phase transitions mirror generalized Z_p lattice gauge theories.

Bulk deconfinement can occur across certain phase transitions.

The number of deconfined excitations can increase after confinement.

Abstract

We study the phase diagrams of a family of 3D "Walker-Wang" type lattice models, which are not topologically ordered but have deconfined anyonic excitations confined to their surfaces. We add a perturbation (analogous to that which drives the confining transition in Z_p lattice gauge theories) to the Walker-Wang Hamiltonians, driving a transition in which all or some of the variables associated with the loop gas or string-net ground states of these models become confined. We show that in many cases the location and nature of the phase transitions involved is exactly that of a generalized Z_p lattice gauge theory, and use this to deduce the basic structure of the phase diagram. We further show that the relationship between the phases on opposite sides of the transition is fundamentally different than in conventional gauge theories: in the Walker-Wang case, the number of species of excitations that are deconfined in the bulk can increase across a transition that confines only some of the species of loops or string-nets. The analogue of the confining transition in the Walker-Wang models can therefore lead to bulk deconfinement and topological order.