The $\mathbb{Z}_2$ toric-code and the double-semion topological order of hardcore Bose-Hubbard-type models in the strong-interaction limit

TL;DR

This paper develops a general framework showing how hardcore Bose-Hubbard models with strong interactions can exhibit $ ext{Z}_2$ toric-code and double-semion topological orders, depending on interaction specifics.

Contribution

It introduces a generic approach to identify conditions under which density-density interactions lead to topological degeneracy and order in strongly interacting Bose-Hubbard models.

Findings

Topological degeneracy arises at specific fractional fillings.

Interaction specifics determine the type of topological order.

Models exhibit long-range entanglement patterns similar to string-net models.

Abstract

We present a generic framework for the emergence of the $\mathbb{Z}_2$ toric-code and the double-semion topological order in a wide class of hardcore Bose-Hubbard-type models governed by density-density interaction and in the strong-interaction regime. We fix fractional filling factor and study under which conditions the density-density interaction gives rise to topological degeneracy. We further specify which dynamics determines the toric-code and the double-semion topological order. Our results indicate that the specifics of the density-density interaction determine the long-range entanglement of the model which possesses "restricted patterns" of the long-range entanglement realized in corresponding string-net models with the same topological order.