FINITELY CORRELATED PURE STATES
Autor(en): | FANNES, M NACHTERGAELE, B WERNER, RF |
Stichwörter: | ALGEBRAS; MAPS; Mathematics; QUANTUM SPIN CHAINS | Erscheinungsdatum: | 1994 | Herausgeber: | ACADEMIC PRESS INC JNL-COMP SUBSCRIPTIONS | Journal: | JOURNAL OF FUNCTIONAL ANALYSIS | Volumen: | 120 | Ausgabe: | 2 | Startseite: | 511 | Seitenende: | 534 | Zusammenfassung: | We study a w*-dense subset of the translation invariant states on an infinite tensor product algebra x Z 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 completely positive map E: A x B --> B. We show that such a state omega 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 omega, and can be expressed in terms of an isometry between suitable tensor product Hilbert spaces. (C) 1994 Academic Press, Inc. |
ISSN: | 00221236 | DOI: | 10.1006/jfan.1994.1041 |
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