G Kells et al J. Stat. Mech. (2009) P03006 doi:10.1088/1742-5468/2009/03/P03006
G Kells, N Moran and J Vala
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We analyze low energy spectral properties of small toroidal configurations of the Kitaev honeycomb spin model in the Abelian topological phase. We begin with a brief classification of honeycomb lattices on a torus. Then, using the Brillouin–Wigner perturbation theory, we explain the low order finite size effects that can occur in these systems and show how they affect their ground state topological degeneracy. Finally, we demonstrate the accuracy of the perturbative method by means of exact diagonalization, and use the insights into the finite size effects to reconstruct the topological degeneracy in a small example system.
75.10.Dg Crystal-field theory and spin Hamiltonians
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
81Q15 Perturbation theories for operators and differential equations
Issue 03 (March 2009)
Received 14 November 2008, accepted for publication 15 December 2008
Published 4 March 2009
G Kells et al J. Stat. Mech. (2009) P03006