An entropic invariant for 2D gapped quantum phases

Understand

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.