Continuous similarity transformation for critical phenomena: Easy-axis antiferromagnetic XXZ model

We apply continuous similarity transformations (CSTs) to the easy-axis antiferromagnetic XXZ-model on square lattice. The CST flow equations are truncated in momentum space by scaling dimension $d$ so that all contributions with $d\le 2$ taken into account. resulting quartic magnon-conserving effective Hamiltonian is analyzed zero-, one-, and two-magnon sector. In this way, a quantitative description of ground-state energy, one-magnon dispersion its gap as well bound states gained for anisotropies ranging from gapped Ising model gapless Heisenberg model. discuss critical properties closing evolution roton mininum. excitation energies calculated their decay continuum determined via inverse participation ratio.