Fermionized Heisenberg model on a non-Bravais lattice with exact local constraint: Application to a honeycomb lattice

We study magnetic order of the Heisenberg model on a non-Bravais lattice based on the Popov - Fedotov trick for exactly treating the local constraint on on-site spin number. The spin operators are represented by auxiliary fermions and an imaginary chemical potential is introduced. The following steps are sketched: i) Parameterizing classical ground state by a magnetic ordering vector and angles between the spins within a unit cell. ii) Going to a local coordinate system. ii) Using functional integral representation with Hubbard-Stratonovich for partition function and calculating determinants of block matrices by Silvester-Powel method. For illustration we obtain some explicit expressions for ferromagnetic Heisenberg model on a honeycomb lattice and compare them with the slave boson results.