Quantum spin chains with quantum group symmetry

被引:17
作者
Fannes, M
Nachtergaele, B
Werner, RF
机构
[1] PRINCETON UNIV, DEPT PHYS, PRINCETON, NJ 08544 USA
[2] UNIV OSNABRUCK, FACHBEREICH PHYS, D-49069 OSNABRUCK, GERMANY
关键词
COMPACT MATRIX PSEUDOGROUPS; C-STAR-ALGEBRAS; HEISENBERG CHAIN; DIFFERENTIAL-CALCULUS; CSTAR-ALGEBRAS; BETHE-ANSATZ; STATES; PRODUCTS; DUALITY; SYSTEMS;
D O I
10.1007/BF02101525
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
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.
引用
收藏
页码:477 / 507
页数:31
相关论文
共 50 条
  • [1] ACCARDI L, 1983, P ROY IRISH ACAD A, V83, P251
  • [2] VALENCE BOND GROUND-STATES IN ISOTROPIC QUANTUM ANTIFERROMAGNETS
    AFFLECK, I
    KENNEDY, T
    LIEB, EH
    TASAKI, H
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1988, 115 (03) : 477 - 528
  • [3] ANISOTROPIC FERROMAGNETIC QUANTUM DOMAINS
    ALCARAZ, FC
    SALINAS, SR
    WRESZINSKI, WF
    [J]. PHYSICAL REVIEW LETTERS, 1995, 75 (05) : 930 - 933
  • [4] [Anonymous], 1979, Operator Algebras and Quantum Statistical Mechanics, DOI [DOI 10.1142/S021798491102698X, 10.1007/978-3-662-09089-3, DOI 10.1007/978-3-662-09089-3]
  • [5] BAAJ S, 1993, ANN SCI ECOLE NORM S, V26, P425
  • [7] Q-DEFORMATIONS OF THE O(3) SYMMETRIC SPIN-1 HEISENBERG CHAIN
    BATCHELOR, MT
    MEZINCESCU, L
    NEPOMECHIE, RI
    RITTENBERG, V
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1990, 23 (04): : L141 - L144
  • [8] BATCHELOR MT, E COMMUNICATION
  • [9] QUANTUM GROUP SYMMETRIES AND NONLOCAL CURRENTS IN 2D QFT
    BERNARD, D
    LECLAIR, A
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1991, 142 (01) : 99 - 138
  • [10] QUANTUM GROUP SYMMETRIES IN 2-DIMENSIONAL LATTICE QUANTUM-FIELD THEORY
    BERNARD, D
    FELDER, G
    [J]. NUCLEAR PHYSICS B, 1991, 365 (01) : 98 - 120