ENTROPY ESTIMATES FOR FINITELY CORRELATED STATES

Abstract

We study in this paper the Renyi entropy densities of integer order for the class of finitely correlated states on a quantum spin chain, and obtain in this way explicit lower bounds for the usual entropy density. We apply this technique to obtain good bounds on the entropy density of a certain state on a spin-3/2 chain. This state is a ground state of a translation invariant nearest neighbour SU(2)-invariant interaction, which is thus shown to posses a residual entropy as T --> 0. Breaking the translation symmetry by adding a small SU(2)-invariant interaction of period two removes the ground state degeneracy, and produces a non-zero spectral gap above the ground state.