Domain wall theory of elementary excitations in anisotropic antiferromagnetic S=1 chains

We present a theoretical investigation of elementary excitations in anisotropic antiferromagnetic S = 1 chains using the concept of domain walls in string (hidden) order. Domain walls are classified by the internal spin projection S-dw(z). We calculate energies and string correlation functions of low lying excited states of the domain wall type in the Haldane phase and compare the results to those of numerical computations. The boundaries of the Haldane phase are determined from the instability of these excitations with respect to the ground state. The interaction between two domain walls is found to be proportional to the product (Sdw,1Sdw,2z)-S-z, it is effectively repulsive for equal spin projections.