Quantum spin chains with quantum group symmetry

verfasst von: Mark Fannes, B. Nachtergaele, R. F. Werner
Abstract: We consider actions of quantum groups on lattice spin systems. We show that if an action of a quantum group respects the local structure of a lattice system, it has to be an ordinary group. Even allowing weakly delocalized (quasi-local) tails of the action, we find that there are no actions of a properly quantum group commuting with lattice translations. The non-locality arises from the ordering of factors in the quantum group C*-algebra, and can be made one-sided, thus allowing semi-local actions on a half chain. Under such actions, localized quantum group invariant elements remain localized. Hence the notion of interactions invariant under the quantum group and also under translations, recently studied by many authors, makes sense even though there is no global action of the quantum group. We consider a class of such quantum group invariant interactions with the property that there is a unique translation invariant ground state. Under weak locality assumptions, its GNS representation carries no unitary representation of the quantum group.
Organisationseinheit(en): Institut für Theoretische Physik
Externe Organisation(en): KU Leuven
Typ: Artikel
Journal: Comm. Math. Phys.
Band: 174
Seiten: 477-507
Anzahl der Seiten: 31
Publikationsdatum: 1996
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
Elektronische Version(en): https://doi.org/10.1007/BF02101525 (Zugang: Unbekannt)

BibTeX

@article{5509032a8fa24ac4a9a3d399a73b680b,
title = "Quantum spin chains with quantum group symmetry",
abstract = "We consider actions of quantum groups on lattice spin systems. We show that if an action of a quantum group respects the local structure of a lattice system, it has to be an ordinary group. Even allowing weakly delocalized (quasi-local) tails of the action, we find that there are no actions of a properly quantum group commuting with lattice translations. The non-locality arises from the ordering of factors in the quantum group C*-algebra, and can be made one-sided, thus allowing semi-local actions on a half chain. Under such actions, localized quantum group invariant elements remain localized. Hence the notion of interactions invariant under the quantum group and also under translations, recently studied by many authors, makes sense even though there is no global action of the quantum group. We consider a class of such quantum group invariant interactions with the property that there is a unique translation invariant ground state. Under weak locality assumptions, its GNS representation carries no unitary representation of the quantum group.",
author = "Mark Fannes and B. Nachtergaele and Werner, {R. F.}",
year = "1996",
doi = "10.1007/BF02101525",
language = "English",
volume = "174",
pages = "477--507",
journal = "Comm. Math. Phys.",
issn = "1432-0916",
publisher = "Springer New York",
number = "3",
}