Dimerization and Solitons in One-Dimensional XY-Z Antiferromagnets

Our previous calculations of the lattice distortion and the formation energy of a soliton in the one-dimensional antiferromagnetic Heisenberg spin-Peierls systems are refined and extended to the case of X Y - Z model. The spin degree of freedom are represented by the phase Hamiltonian with the help of boson representation of fermions introduced by the Jordan-Wigner transformation. Parameters in this phase Hamiltonian are adjusted so that spin wave velocity and exponent of correlation function agree with exact results. This adjustment is shown to give also exact spin susceptibility in the absence of lattice distortion. Based on this phase Hamiltonian of the X Y - Z model localized excitations (solitons) in the presence of lattice distortions are examined in details including the width, the formation energy and the magnetic field dependence.