Perturbative study of the Kitaev model with spontaneous time-reversal symmetry breaking

Sébastien Dusuel, Kai Phillip Schmidt, Julien Vidal, and Rosa Letizia Zaffino
Phys. Rev. B 78, 125102 – Published 5 September 2008

Abstract

We analyze the Kitaev model on the triangle-honeycomb lattice whose ground state has recently been shown to be a chiral spin liquid. We consider two perturbative expansions: the isolated-dimer limit containing Abelian anyons and the isolated-triangle limit. In the former case, we derive the low-energy effective theory and discuss the role played by multiplaquette interactions. In this phase, we also compute the spin-spin correlation functions for any vortex configuration. In the isolated-triangle limit, we show that the effective theory is, at lowest nontrivial order, the Kitaev honeycomb model at the isotropic point. We also compute the next-order correction which opens a gap and yields non-Abelian anyons.

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  • Received 30 April 2008

DOI:https://doi.org/10.1103/PhysRevB.78.125102

©2008 American Physical Society

Authors & Affiliations

Sébastien Dusuel1,*, Kai Phillip Schmidt2,†, Julien Vidal3,‡, and Rosa Letizia Zaffino3,§

  • 1Lycée Louis Thuillier, 70 Boulevard de Saint Quentin, 80098 Amiens Cedex 3, France
  • 2Lehrstuhl für theoretische Physik, Otto-Hahn-Straße 4, D-44221 Dortmund, Germany
  • 3Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France

  • *sdusuel@gmail.com
  • schmidt@fkt.physik.uni-dortmund.de
  • vidal@lptmc.jussieu.fr
  • §zaffino@lptmc.jussieu.fr

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Issue

Vol. 78, Iss. 12 — 15 September 2008

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