Kitaev model and dimer coverings on the honeycomb lattice

TL;DR

This paper extends the Kitaev honeycomb model by exploring various dimer coverings, analyzing their phase diagrams and vortex interactions, revealing both similarities and differences with the original model.

Contribution

It introduces new dimer coverings in the Kitaev model and analyzes their ground states and vortex properties, expanding understanding of the model's phase space.

Findings

Different dimer coverings exhibit varied vortex interactions.

Vortex-vortex interactions can be attractive or repulsive depending on the covering.

Qualitative differences are supported by high-order perturbative calculations.

Abstract

We consider an extension of the Kitaev honeycomb model based on arbitrary dimer coverings satisfying matching rules. We focus on three different dimer coverings having the smallest unit cells for which we calculate the ground-state phase diagram. We also study one- and two-vortex properties for these coverings in the Abelian phases and show that vortex-vortex interactions can be attractive or repulsive. These qualitative differences are confirmed analytically by high-order perturbative expansions around the isolated-dimer limit. Similarities and differences with the original Kitaev honeycomb model are discussed.