On spectral properties of the uniaxially anisotropic Heisenberg Hamiltonian

Abstract

The uniaxially anisotropic Heisenberg Hamiltonian H is considered, which describes a simple lattice of spins and incorporates first-nearest, ..., m-nearest neighbour interactions under the condition that Jjαj ≥ 0, j = 1, ..., m, where Jj, αj are the exchange and anisotropy constants of the j-th shell of neighbours, respectively. It is proved that, there are no bound states in the two-magnon space above the band of the continuous spectrum of H and, for the XY model, there are no two-magnon bound states at all.