Hardcore Magnons in the S=1/2 Heisenberg Model on the Square Lattice

We propose a versatile approach to treat commonly arising constraints. It is illustrated for interacting magnons of the Heisenberg antiferromagnet on a square lattice. For systems of $L\times L$ sites a non-perturbative continuous unitary transformation (CUT) is used to derive an effective Hamiltonian conserving the number of magnons. They are bosonic particles with a hardcore constraint which is captured by a local, repulsive interaction U. The limits $U\to \mathrm{\infty }$ and $L\to \mathrm{\infty }$ are achieved by extrapolation. The residual spin gap ${\mathrm{\Delta }}_1$ is smaller than 0.01J reflecting the gapless nature of the magnons. The one-magnon dispersion displays all known characteristics.