An entropic invariant for 2D gapped quantum phases

TL;DR

This paper introduces an entropic invariant for 2D gapped quantum phases that captures topological order and is invariant under local quantum circuits, demonstrated through Kitaev's models.

Contribution

It defines a new entropic quantity based on operator algebras that characterizes gapped quantum phases and matches the topological entanglement entropy for specific models.

Findings

The invariant is explicitly calculated for Kitaev's quantum double models.

The quantity is invariant under constant-depth local quantum circuits.

It provides a new method to identify topological order without extracting TEE directly.

Abstract

We introduce an entropic quantity for two-dimensional (2D) quantum spin systems to characterize gapped quantum phases modeled by local commuting projector code Hamiltonians. The definition is based on a recently introduced specific operator algebra defined on an annular region, which encodes the superselection sectors of the model. The quantity is calculable from local properties, and it is invariant under any constant-depth local quantum circuit, and thus an indicator of gapped quantum spin-liquids. We explicitly calculate the quantity for Kitaev's quantum double models, and show that the value is exactly same as the topological entanglement entropy of the models. Our method circumvents some of the problems around extracting the TEE, allowing us to prove invariance under constant-depth quantum circuits.