Self-duality and bound states of the toric code model in a transverse field

Vidal J, Thomale R, Schmidt KP, Dusuel S (2009)

Publication Status: Published

Publication Type: Journal article

Publication year: 2009

Journal

Physical Review B American Physical Society

Publisher: AMER PHYSICAL SOC

Book Volume: 80

Journal Issue: 8

DOI: 10.1103/PhysRevB.80.081104

Abstract

We investigate the effect of a transverse magnetic field on the toric code model. We show that this problem can be mapped onto the Xu-Moore model and thus onto the quantum compass model, which are known to be self-dual. We analyze the low-energy spectrum by means of perturbative continuous unitary transformations and determine accurately the energy gaps of various symmetry sectors. Our results are in very good agreement with exact diagonalization data for all values of the parameters except at the self-dual point where level crossings are responsible for a first-order phase transition between a topological phase and a polarized phase. Interestingly, bound states of two and four quasiparticles with fermionic and bosonic statistics emerge, and display dispersion relations of reduced dimensionality.

Authors with CRIS profile

Kai Phillip Schmidt Professur für Theoretische Physik

Involved external institutions

University of Paris 6 - Pierre et Marie Curie / Université Paris VI Pierre et Marie Curie (UPMC) FR France (FR) Karlsruhe Institute of Technology (KIT) DE Germany (DE) Lycée Saint-Louis FR France (FR)

How to cite

APA:

Vidal, J., Thomale, R., Schmidt, K.P., & Dusuel, S. (2009). Self-duality and bound states of the toric code model in a transverse field. Physical Review B, 80(8). https://doi.org/10.1103/PhysRevB.80.081104

MLA:

Vidal, Julien, et al. "Self-duality and bound states of the toric code model in a transverse field." Physical Review B 80.8 (2009).

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