Frustrated topological symmetry breaking: geometrical frustration and anyon condensation

TL;DR

This paper explores how geometrical frustration influences phase transitions in topological lattice models, revealing complex phases with combined topological and symmetry-breaking orders, and characterizing these transitions with effective models and numerical methods.

Contribution

It introduces effective models for frustrated topological phases and analyzes phase transitions using exact diagonalization and series expansion techniques.

Findings

Identification of phases with coexisting topological and translational symmetry-breaking order.

Discovery of phase transitions driven by geometrical frustration in topological models.

Characterization of both Abelian and non-Abelian topological phases within the phase diagram.

Abstract

We study the phase diagram of a topological string-net type lattice model in the presence of geometrically frustrated interactions. These interactions drive several phase transitions that reduce the topological order, leading to a rich phase diagram including both Abelian ($\mathbb{Z}_2$) and non-Abelian ($\text{Ising}\times \overline{\text{Ising}}$) topologically ordered phases, as well as phases with broken translational symmetry. Interestingly, one of these phases simultaneously exhibits (Abelian) topological order and long-ranged order due to translational symmetry breaking, with non-trivial interactions between excitations in the topological order and defects in the long-ranged order. We introduce a variety of effective models, valid along certain lines in the phase diagram, which can be used to characterize both topological and symmetry-breaking order in these phases, and in many cases allow us to characterize the phase transitions that separate them. We use exact diagonalization and high-order series expansion to study areas of the phase diagram where these models break down, and to approximate the location of the phase boundaries.