Condensation of achiral simple currents in topological lattice models: a Hamiltonian study of topological symmetry breaking

TL;DR

This paper constructs Hamiltonians for topological phase transitions in 2+1D systems, revealing how topological order changes via condensation, with mappings to Potts models and implications for doubled Chern-Simons theories.

Contribution

It explicitly constructs Hamiltonians connecting different topologically ordered phases and analyzes the phase transitions and excitations involved.

Findings

Hamiltonians for topological phase transitions are explicitly constructed.

Low-energy behavior near transitions maps onto Potts models.

Condensed phases exhibit split excitations from original topological theories.

Abstract

We describe a family of phase transitions connecting phases of differing non-trivial topological order by explicitly constructing Hamiltonians of the Levin-Wen[PRB 71, 045110] type which can be tuned between two solvable points, each of which realizes a different topologically ordered phase. We show that the low-energy degrees of freedom near the phase transition can be mapped onto those of a Potts model, and we discuss the stability of the resulting phase diagram to small perturbations about the model. We further explain how the excitations in the condensed phase are formed from those in the original topological theory, some of which are split into multiple components by condensation, and we discuss the implications of our results for understanding the nature of general achiral topological phases in 2+1 dimensions in terms of doubled Chern-Simons theories.