Finitely correlated states on quantum spin chains

verfasst von: M. Fannes, B. Nachtergaele, R. F. Werner
Abstract: We study a construction that yields a class of translation invariant states on quantum spin chains, characterized by the property that the correlations across any bond can be modeled on a finite-dimensional vector space. These states can be considered as generalized valence bond states, and they are dense in the set of all translation invariant states. We develop a complete theory of the ergodic decomposition of such states, including the decomposition into periodic Néel ordered states. The ergodic components have exponential decay of correlations. All states considered can be obtained as local functions of states of a special kind, so-called purely generated states, which are shown to be ground states for suitably chosen finite range VBS interactions. We show that all these generalized VBS models have a spectral gap. Our theory does not require symmetry of the state with respect to a local gauge group. In particular we illustrate our results with a one-parameter family of examples which are not isotropic except for one special case. This isotropic model coincides with the one-dimensional antiferomagnet, recently studied by Affleck, Kennedy, Lieb, and Tasaki.
Organisationseinheit(en): Institut für Theoretische Physik
Typ: Artikel
Journal: Comm. Math. Phys.
Band: 144
Seiten: 443-490
Anzahl der Seiten: 48
Publikationsdatum: 1992
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja

BibTeX

@article{14ff30549e374ef49837d2d253356f48,
title = "Finitely correlated states on quantum spin chains",
abstract = "We study a construction that yields a class of translation invariant states on quantum spin chains, characterized by the property that the correlations across any bond can be modeled on a finite-dimensional vector space. These states can be considered as generalized valence bond states, and they are dense in the set of all translation invariant states. We develop a complete theory of the ergodic decomposition of such states, including the decomposition into periodic N{\'e}el ordered states. The ergodic components have exponential decay of correlations. All states considered can be obtained as local functions of states of a special kind, so-called purely generated states, which are shown to be ground states for suitably chosen finite range VBS interactions. We show that all these generalized VBS models have a spectral gap. Our theory does not require symmetry of the state with respect to a local gauge group. In particular we illustrate our results with a one-parameter family of examples which are not isotropic except for one special case. This isotropic model coincides with the one-dimensional antiferomagnet, recently studied by Affleck, Kennedy, Lieb, and Tasaki.",
author = "M. Fannes and B. Nachtergaele and Werner, {R. F.}",
year = "1992",
language = "Undefined/Unknown",
volume = "144",
pages = "443--490",
journal = "Comm. Math. Phys.",
issn = "1432-0916",
publisher = "Springer New York",
number = "3",
}