Abundance of translation invariant pure states on quantum spin chains (Q1196105)

Let \(Z\) be a one-dimensional lattice and let \(A\) be the observable algebra corresponding to \(Z\) and describing a quantum spin chain. The authors have proved that the set of pure transition invariant states is \(w^*\)-dense in the set of all transition invariant states of \(A\). Moreover, it is shown, that every transition invariant state can be approximated by pure transition invariant states having an exponential decay of correlation.