  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.
