Bound states in two-dimensional spin systems near the Ising limit: A quantum finite-lattice study

Sébastien Dusuel, Michael Kamfor, Kai Phillip Schmidt, Ronny Thomale, and Julien Vidal
Phys. Rev. B 81, 064412 – Published 17 February 2010

Abstract

We analyze the properties of low-energy bound states in the transverse-field Ising model and in the XXZ model on the square lattice. To this end, we develop an optimized implementation of perturbative continuous unitary transformations. The Ising model is studied in the small-field limit which is found to be a special case of the toric code model in a magnetic field. To analyze the XXZ model, we perform a perturbative expansion about the Ising limit in order to discuss the fate of the elementary magnon excitations when approaching the Heisenberg point.

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  • Received 8 December 2009

DOI:https://doi.org/10.1103/PhysRevB.81.064412

©2010 American Physical Society

Authors & Affiliations

Sébastien Dusuel1,*, Michael Kamfor2,†, Kai Phillip Schmidt2,‡, Ronny Thomale2,3,4,§, and Julien Vidal5,∥

  • 1Lycée Saint-Louis, 44 Boulevard Saint-Michel, 75006 Paris, France
  • 2Lehrstuhl für Theoretische Physik I, Otto-Hahn-Straße 4, TU Dortmund, 44221 Dortmund, Germany
  • 3Institut für Theorie der Kondensierten Materie, Universität Karlsruhe, D-76128 Karlsruhe, Germany
  • 4Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
  • 5Laboratoire 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
  • kamfor@fkt.physik.uni-dortmund.de
  • schmidt@fkt.physik.uni-dortmund.de
  • §rthomale@princeton.edu
  • vidal@lptmc.jussieu.fr

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Vol. 81, Iss. 6 — 1 February 2010

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