92-132 M.Fannes , B.Nachtergaele , R.F.Werner

Finitely Correlated Pure States (75K, Plain TeX) Oct 6, 92

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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.

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