M.Fannes , B.Nachtergaele , R.F.Werner
Finitely Correlated Pure States
(75K, Plain TeX)
ABSTRACT. We study a w*-dense subset of the translation invariant states on an
infinite tensor product algebra $\bigotimes_\Ir\A$, where $\A$ is a
matrix algebra. These ``finitely correlated states'' are explicitly
constructed in terms of a finite dimensional auxiliary algebra $\B$
and a \cp\ map $\E:\A\otimes\B\to\B$. We show that such a state
$\om$ is pure if and only if it is extremal periodic and its entropy
density vanishes. In this case the auxiliary objects $\B$ and $\E$ are
uniquely determined by $\om$, and can be expressed in terms of an
isometry between suitable tensor product Hilbert spaces.