Exactly Solvable Models for Symmetry-Enriched Topological Phases

TL;DR

This paper develops exactly solvable models for a broad class of bosonic symmetry-enriched topological phases, providing a systematic way to construct fixed-point wave functions and Hamiltonians for both unitary and anti-unitary symmetries.

Contribution

It introduces a unified construction method for SET phases, extending to anti-unitary symmetries and anomalous cases, generalizing group extensions of fusion categories.

Findings

Constructed fixed-point wave functions and Hamiltonians for SET phases.

Extended the framework to anti-unitary and mirror symmetries.

Provided a mathematical generalization of group extensions for fusion categories.

Abstract

We construct fixed-point wave functions and exactly solvable commuting-projector Hamiltonians for a large class of bosonic symmetry-enriched topological (SET) phases, based on the concept of equivalent classes of symmetric local unitary transformations. We argue that for onsite unitary symmetries, our construction realizes all SETs free of anomaly, as long as the underlying topological order itself can be realized with a commuting-projector Hamiltonian. We further extend the construction to anti-unitary symmetries (e.g. time-reversal symmetry), mirror-reflection symmetries, and to anomalous SETs on the surface of three-dimensional symmetry-protected topological phases. Mathematically, our construction naturally leads to a generalization of group extensions of unitary fusion categories to anti-unitary symmetries.