ArticleOriginal scientific text

Title

Positive energy representations for quantum spin models in 1+1 dimensions

Authors 1

Affiliations

  1. Graduate School of Mathematics, Kyushu University, Hakozaki, Fukuoka, Japan

Abstract

We present recent results on positive energy representations of quantum spin models.

Bibliography

  1. I. Affleck, T. Kennedy, E. H. Lieb and H. Tasaki, Valence Bond Ground States in Isotropic Quantum Antiferromagnets, Commun. Math. Phys. 115 (1988), 477-528.
  2. S. R. Alcaraz, R. S. Salinas and W. F. Wreszinski, Anisotropic ferromagnetic quantum domain, Phys. Rev. Lett. 75 (1995), 930-933.
  3. H. Araki, Soliton sector of the XY-model, International Journal of Modern Physics B 10, Nos 13 & 14 (1996), 1685-1693.
  4. H. Araki and T. Matsui, Ground states of the XY model, Commun. Math. Phys. 101 (1985), 213-245.
  5. O. Bratteli, A. Kishimoto and D. Robinson, Ground states of quantum spin systems, Commun. Math. Phys. 64 (1978), 41-48.
  6. O. Bratteli and D. Robinson, Operator algebras and quantum statistical mechanics II, Springer, 1997.
  7. M. Fannes, B. Nachtergaele and R. Werner, Finitely Correlated States on Quantum Spin Chains, Commun. Math. Phys. 144 (1992), 443-490.
  8. J. Frölich, New superselection sectors (soliton states) in two dimensional Bose quantum field theory, Commun. Math. Phys. 47 (1976), 269-310.
  9. C. T. Gottstein and R. Werner, Zero-energy states of the ferromagnetic XXZ chain, preprint, Osnabrück 1995.
  10. C. T. Gottstein and R. Werner, Zero-energy ground states of quantum lattice systems, preprint, Osnabrück 1995.
  11. R. Haag, Local Quantum Physics, Springer-Verlag, 1992.
  12. T. Koma and B. Nachtergaele, The spectral gap of the ferromagnetic XXZ chain, Lett. Math. Phys. 40 (1997), 1-16.
  13. T. Koma and B. Nachtergaele, preprint.
  14. T. Matsui, Translationally Symmetry Breaking and Soliton Sectors for Massive Quantum Spin Models in 1+1 Dimensions, Commun. Math. Phys. 189 (1997), 127-144.
  15. T. Matsui, On the spectrum of the kink of the ferromagnetic XXZ model, to appear in Lett. Math. Phys.
  16. T. Matsui, On ground states of the one-dimensional ferromagnetic XXZ model, Lett. Math. Phys. 37 (1996), 397-403.
  17. D. Schlingemann, On algebraic theory of soliton and anti-soliton sectors, Rev. Math. Phys. 8 (1996), 301-326.
Pages:
309-320
Main language of publication
English
Published
1998
Exact and natural sciences