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

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

2009-02-20

arxiv.org/abs/0902.3547v3

Phys.Rev.B80:081104,2009

Physics

Condensed Matter

Other Condensed Matter

4 pages, 4 figures, typos in Eq.(4) corrected

Scientific paper

10.1103/PhysRevB.80.081104

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.

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