Approximate solution of the heisenberg antiferromagnet in a triangular lattice

Abstract

The anisotropic antiferromagnetic Heisenberg model in a triangular lattice is solved approximately using the pair non-magnetic excitation theory (PNME) which was generalized in order to apply to non-bipartite lattices. The ground energy state E g , eigenfunction and excitations energies are obtained for arbitrary spin and anisotropy. In particular, for the isotropic case and spin 1 2 , E g = −0.172. This value corresponds to a 6% error when compared with the exact value obtained numerically from small cluster calculations and compares successfully with energies obtained by other methods. A parametric phase transition for ordered - disordered ground state is obtained as function of the spin and anisotropy.