  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 model 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.
