Isolated eigenvalues of the ferromagneticspin-J XXZ chain with kink boundary conditions

Abstract

We investigate the low-lying excited states of the spinJ ferromagneticXXZ chain withIsing anisotropy Δ and kink boundary conditions. Since the third component of the total magnetization,M, is conserved, it is meaningful to study the spectrum for each fixed value ofM. We provethat for J≥3/2 the lowest excited eigenvalues are separated by a gap from the rest of the spectrum,uniformly in the length of the chain. In the thermodynamic limit, this means that there area positive number of excitations above the ground state and below the essential spectrum.