Exact Antiferromagnetic Ground States of Quantum Spin Chains

We recall a simple class of translation invariant states for an infinite quantum spin chain, which was introduced by L. Accardi. Those states have exponential decay of correlation functions, and a subclass contains the ground states of a certain class of finite range interactions. We consider, in particular, a family of states for integer spin chains, containing as its simplest member the ground state of a spin 1 Heisenberg antiferromagnet recently studied by I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki. For this family we compute explicitly the correlation functions and other properties