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

Abstract

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.

5 pages, 3 figures, typos in Eq.(6) corrected

References in corpus (5)

• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
• Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices
• Adiabatic Preparation of Topological Order
• Anyonic interferometry and protected memories in atomic spin lattices
• Emergent Fermions and Anyons in the Kitaev Model

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