Details
| Original language | English |
|---|---|
| Pages (from-to) | 511-534 |
| Number of pages | 24 |
| Journal | J. Funct. Anal. |
| Volume | 120 |
| Issue number | 2 |
| Publication status | Published - 1994 |
Abstract
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In: J. Funct. Anal., Vol. 120, No. 2, 1994, p. 511-534.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Finitely correlated pure states
AU - Fannes, M.
AU - Nachtergaele, B.
AU - Werner, R. F.
PY - 1994
Y1 - 1994
N2 - We study a w*-dense subset of the translation invariant states on an infinite tensor product algebra Aotimes Z, 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 otimes B to 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 and can be expressed in terms of an isometry between suitable tensor product Hilbert spaces.
AB - We study a w*-dense subset of the translation invariant states on an infinite tensor product algebra Aotimes Z, 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 otimes B to 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 and can be expressed in terms of an isometry between suitable tensor product Hilbert spaces.
M3 - Article
VL - 120
SP - 511
EP - 534
JO - J. Funct. Anal.
JF - J. Funct. Anal.
SN - 1096-0783
IS - 2
ER -