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Communications in Mathematical Physics

, Volume 174, Issue 3, pp 477–507 | Cite as

Quantum spin chains with quantum group symmetry

  • M. Fannes
  • B. Nachtergaele
  • R. F. Werner
Article

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 groupC*-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.

Keywords

Quantum Group Unitary Representation Spin Chain Lattice Spin Weak Locality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • M. Fannes
    • 1
    • 2
  • B. Nachtergaele
    • 3
  • R. F. Werner
    • 4
  1. 1.Inst. Theor. FysicaUniversiteit LeuvenHeverleeBelgium
  2. 2.OnderzoeksleiderN.F.W.O.Belgium
  3. 3.Dept. of PhysicsPrinceton UniversityPrincetonUSA
  4. 4.Fachbereich PhysikUniversität OsnabrückOsnabrückGermany

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