Elementary excitations in one-dimensional spin-orbit models: Neutral and charged solitons and their bound states

Abstract

We study, both numerically and variationally, the interplay between different types of elementary excitations in the model of a spin chain with anisotropic spin-orbit coupling, in the vicinity of the ``dimer line'' with an exactly known dimerized ground state. Our variational treatment is found to be in a qualitative agreement with the exact diagonalization results. Soliton pairs are shown to be the lowest excitations only in a very narrow region of the phase diagram near the dimer line, and the phase transitions are always governed by magnon-type excitations which can be viewed as soliton-antisoliton bound states. It is shown that when the anisotropy exceeds certain critical value, an additional phase boundary appears. In the doped model on the dimer line, the exact elementary charge excitation is shown to be a hole bound to a soliton. Bound states of those ``charged solitons'' are studied; exact solutions for N-hole bound states are presented.