We investigate the effect of a transverse magnetic field on the toric codemodel. We show that this problem can be mapped onto the Xu-Moore model and thusonto the quantum compass model which are known to be self-dual. We analyze thelow-energy spectrum by means of perturbative continuous unitary transformationsand determine accurately the energy gaps of various symmetry sectors. Ourresults are in very good agreement with exact diagonalization data for allvalues of the parameters except at the self-dual point where level crossingsare responsible for a first order phase transition between a topological phaseand a polarized phase. Interestingly, bound states of two and fourquasiparticles with fermionic and bosonic statistics emerge, and displaydispersion relations of reduced dimensionality.
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