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

Understand

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.