Drinfeld Center as Quantum State Monodromy over Bloch Hamiltonians around Defects

TL;DR

This paper connects the mathematical structure of the Drinfeld center to the topological order of quantum states near defects in fractional topological insulators, revealing a new way to understand their monodromy.

Contribution

It demonstrates how the fusion rules of the Drinfeld center $ ext{Vec}_G$ model the local topological order around defects in the Brillouin zone of fractional topological insulators.

Findings

$ ext{Vec}_G$ fusion rules describe topological order near defects.

Monodromy of gapped states relates to $ ext{Vec}_G$ structure.

Local topological properties are captured by the Drinfeld center.

Abstract

The Drinfeld center fusion category $\mathcal{Z}(\mathrm{Vec}_G)$ famously models anyons in certain lattice models. Here we demonstrate how its fusion rules may also describe topological order in fractional topological insulator materials, in the vicinity of point defects in the Brillouin zone. Concretely, we prove that $\mathcal{Z}(\mathrm{Vec}_G)$ reflects, locally over a punctured disk in the Brillouin zone, the monodromy (topological order) of gapped quantum states over the parameter space of Bloch Hamiltonians whose classifying space has fundamental group $G$.