Spin excitations in the Kitaev-Heisenberg model: Popov-Fedotov fermionization

Abstract

Abstract We study a Kitaev-Heisenberg model of spin 1/2 using the Popov-Fedotov fermionization proccedure. We derive the free energy of the quantum spin system on a Bravais lattice within one-loop approximation with exact on-site constraint. We discuss the obtained magnetic excitation spectrum for a particular case of square lattice in relation to the data derived by the equation of motion method and with the result of the linear spin wave theory in Holstein - Primakoff representation.