Quantum solitons and the Haldane phase in antiferromagnetic spin chains

A survey is given of the relevance of solitons for the present understanding of antiferromagnetic quantum spin chains. For the -chain the basic elementary excitations are solitons. Two solitons combine to form a magnon and its internal degree of freedom is observed as an excitation continuum. For S = 1 chains the existence of the massive Haldane phase is related to the dissociation of soliton pairs (pairs of domain walls with respect to antiferromagnetic order). Based on the hidden (or string) order, the appropriate mean field theory for antiferromagnetic S = 1 chains is introduced as based on uncorrelated solitons and applied to calculate correlation functions. It is described how to include correlations between solitons using an approximate mapping to an effective chain. The basic elementary excitations in the Haldane phase are identified as solitons with respect to the hidden order.