Dynamical correlation functions of the toric code in a uniform magnetic field are studied inside the topological phase, in the small-field limit. Such an experimentally measurable quantity displays rich field-dependent features that can be understood
via the interplay of the kinetics and the interaction of the anyonic excitations. In particular, it is sensitive to the two-quasiparticle bound states that are present in the spectrum for a wide range of magnetic fields. Interestingly, such collective modes can even constitute the lowest-energy excitations of the system.
We consider noninteracting fermions on the honeycomb lattice in the presence of a magnetic vortex superlattice. It is shown that depending on the superlattice periodicity, a gap may open at zero energy. We derive an expression of the gap in the small
-flux limit but the main qualitative features are found to be valid for arbitrary fluxes. This study provides an original example of a metal-insulator transition induced by a strongly modulated magnetic field in graphene. At the same time our results directly apply to Kitaevs honeycomb model in a vortex superlattice.
We analyze the properties of low-energy bound states in the transverse-field Ising model and in the XXZ model on the square lattice. To this end, we develop an optimized implementation of perturbative continuous unitary transformations. The Ising mod
el is studied in the small-field limit which is found to be a special case of the toric code model in a magnetic field. To analyze the XXZ model, we perform a perturbative expansion about the Ising limit in order to discuss the fate of the elementary magnon excitations when approaching the Heisenberg point.
