Emergent Fermions and Anyons in the Kitaev Model

Kai Phillip Schmidt, Sébastien Dusuel, and Julien Vidal
Phys. Rev. Lett. 100, 057208 – Published 8 February 2008

Abstract

We study the gapped phase of the Kitaev model on the honeycomb lattice using perturbative continuous unitary transformations. The effective low-energy Hamiltonian is found to be an extended toric code with interacting anyons. High-energy excitations are emerging free fermions which are composed of hard-core bosons with an attached string of spin operators. The excitation spectrum is mapped onto that of a single particle hopping on a square lattice in a magnetic field. We also illustrate how to compute correlation functions in this framework. The present approach yields analytical perturbative results in the thermodynamical limit without using the Majorana or the Jordan-Wigner fermionization initially proposed to solve this problem.

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  • Received 19 September 2007

DOI:https://doi.org/10.1103/PhysRevLett.100.057208

©2008 American Physical Society

Authors & Affiliations

Kai Phillip Schmidt1,*, Sébastien Dusuel2,†, and Julien Vidal3,‡

  • 1Institute of Theoretical Physics, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
  • 2Lycée Louis Thuillier, 70 Boulevard de Saint Quentin, 80098 Amiens Cedex 3, France
  • 3Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France

  • *kaiphillip.schmidt@epfl.ch
  • sdusuel@gmail.com
  • vidal@lptmc.jussieu.fr

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Vol. 100, Iss. 5 — 8 February 2008

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