Low-energy effective theory of the toric code model in a parallel field

Details Low-energy effective theory of the toric code model in a parallel field Low-energy effective theory of the toric code model in a parallel field

2008-07-03

arxiv.org/abs/0807.0487v3

Phys.Rev.B79:033109,2009

Physics

Condensed Matter

Other Condensed Matter

5 pages, 3 figures, typos in Eq.(8) corrected

Scientific paper

10.1103/PhysRevB.79.033109

We determine analytically the phase diagram of the toric code model in a parallel magnetic field which displays three distinct regions. Our study relies on two high-order perturbative expansions in the strong- and weak-field limit, as well as a large-spin analysis. Calculations in the topological phase establish a quasiparticle picture for the anyonic excitations. We obtain two second-order transition lines that merge with a first-order line giving rise to a multicritical point as recently suggested by numerical simulations. We compute the values of the corresponding critical fields and exponents that drive the closure of the gap. We also give the one-particle dispersions of the anyonic quasiparticles inside the topological phase.

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