Easy-plane anisotropic-exchange honeycomb magnets: quantum effects and dealing with them

We attempt a study of magnetic spectrum of the easy-plane anisotropic spin model on a honeycomb lattice with bond-dependent exchange interactions, which can be related to the extended Kitaev-Heisenberg model through the axes transformation. We find signatures of strong magnon-magnon interactions in both zero-field zigzag state, and the paramagnetic polarized phase. First, we show that the zigzag state is unstable towards magnon decays due to anisotropic terms. Next, we calculate self-energy in the first order of 1/S approximation in the polarized phase, find strong renormalization of the real part of the spectrum near the critical point, and propose a novel way to regularize unphysical divergences. Finally, we obtain dynamical spin structure factor at the Γ point in the polarized phase, compare it to ESR and Raman experiments and show that the spectrum has features similar to those observed experimentally, such as (i) downward renormalization of the magnon mode due to repulsion from the two-magnon continuum, down to gap closure, and (ii) redistribution of the spectral weight from single magnon mode to the continuum.