ArticleOriginal scientific text
Title
Positive energy representations for quantum spin models in 1+1 dimensions
Authors 1
Affiliations
- Graduate School of Mathematics, Kyushu University, Hakozaki, Fukuoka, Japan
Abstract
We present recent results on positive energy representations of quantum spin models.
Bibliography
- 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.
- S. R. Alcaraz, R. S. Salinas and W. F. Wreszinski, Anisotropic ferromagnetic quantum domain, Phys. Rev. Lett. 75 (1995), 930-933.
- H. Araki, Soliton sector of the XY-model, International Journal of Modern Physics B 10, Nos 13 & 14 (1996), 1685-1693.
- H. Araki and T. Matsui, Ground states of the XY model, Commun. Math. Phys. 101 (1985), 213-245.
- O. Bratteli, A. Kishimoto and D. Robinson, Ground states of quantum spin systems, Commun. Math. Phys. 64 (1978), 41-48.
- O. Bratteli and D. Robinson, Operator algebras and quantum statistical mechanics II, Springer, 1997.
- M. Fannes, B. Nachtergaele and R. Werner, Finitely Correlated States on Quantum Spin Chains, Commun. Math. Phys. 144 (1992), 443-490.
- J. Frölich, New superselection sectors (soliton states) in two dimensional Bose quantum field theory, Commun. Math. Phys. 47 (1976), 269-310.
- C. T. Gottstein and R. Werner, Zero-energy states of the ferromagnetic XXZ chain, preprint, Osnabrück 1995.
- C. T. Gottstein and R. Werner, Zero-energy ground states of quantum lattice systems, preprint, Osnabrück 1995.
- R. Haag, Local Quantum Physics, Springer-Verlag, 1992.
- T. Koma and B. Nachtergaele, The spectral gap of the ferromagnetic XXZ chain, Lett. Math. Phys. 40 (1997), 1-16.
- T. Koma and B. Nachtergaele, preprint.
- T. Matsui, Translationally Symmetry Breaking and Soliton Sectors for Massive Quantum Spin Models in 1+1 Dimensions, Commun. Math. Phys. 189 (1997), 127-144.
- T. Matsui, On the spectrum of the kink of the ferromagnetic XXZ model, to appear in Lett. Math. Phys.
- T. Matsui, On ground states of the one-dimensional ferromagnetic XXZ model, Lett. Math. Phys. 37 (1996), 397-403.
- D. Schlingemann, On algebraic theory of soliton and anti-soliton sectors, Rev. Math. Phys. 8 (1996), 301-326.