On kink states of ferromagnetic chains

Abstract

We study kink states of quantum, ferromagnetic, easy axis spin 1/2 chains at zero temperature. These are produced by applying opposite magnetic fields on the two end sites of the chain. For sufficiently strong anisotropy and boundary field, we obtain estimates on the wave function of the lowest energy states in sectors with fixed third component of the total spin. These estimates imply that the magnetization profile has a kink structure with a well-defined location and a finite width. The energies of kink states in different sectors are exponentially close as long as they are not located near the boundaries. The basic tool that we use here is the principle of exponential localization of eigenvectors. We illustrate the method in the simplest case of the Heisenberg XXZ model and then show how it can be generalized to more complicated models. In the particular case of the Heisenberg XXZ model our results are consistent with the exact kink wave functions known for a special value of the boundary magnetic field.