Kitaev model and dimer coverings on the honeycomb lattice

2010/05/31 by M. Kamfor, Michael Kamfor, Sébastien Dusuel +5
Engineering · Mathematics · Physics and Astronomy · #Abelian group #Advanced Condensed Matter Physics #Combinatorics #Condensed matter physics #Dimer #Geometry #Honeycomb #Lattice (music) #Mathematics #Mechanics #Perovskite Materials and Applications #Phase (matter) #Phase diagram #Physics #Physics of Superconductivity and Magnetism #Pure mathematics #Quantum mechanics #Theoretical physics #Vortex #cond-mat.other #quant-ph

paper · pdf · doi:10.1088/1742-5468/2010/08/p08010

published as J.Stat.Mech.1008:P08010,2010 · 8 pages, 9 figures, published version

openalex publication_date 2010/08/12 · arxiv created 2010/08/23 · arxiv updated 2014/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

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