Translational Symmetry Breaking and Soliton Sectors for Massive Quantum Spin Models in 1 + 1 Dimensions

We consider the classification of pure infinite volume ground states and that of soliton sectors for 1+1 dimensional massive quantum spin models. We obtain a proof that non-translationally invariant ground state cannot exist for a class of translationally invariant Hamiltonians including the spin 1 AKLT (Affleck Kennedy Lieb Tasaki) antiferromagnetic spin model. We also obtain a complete classification of soliton sectors (up to unitary equivalence) for certain massive models (e.g. ferromagnetic XXZ models). Received: 13 January 1997 / Accepted: 11 March 1997