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Properties of propagation of quantum spin systems

Published online by Cambridge University Press:  17 February 2009

Derek W. Robinson
Derek W. Robinson
Affiliation:
Département de Physique Université d'Aix-Marseille II, Luminy, Marseille Centre de Physique Théorique, CNRS, Marseille France and Department of Mathematical Physics, University of Adelaide, South Australia, 5001.
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Abstract

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Using an estimate on the group velocity we give an independent proof of the existence of time translations for a large class of short range interactions. We demonstrate that these systems satisfy a strong form of causal propagation and that space-time algebras in suitable space-like directions are disjoint. Finally we derive criteria for dispersion of the interaction in terms of the algebraic density of the orbit of local subalgebras under the evolution or under the associated group of shifts. In this sense the Heisenberg and X-Y models are dispersive but the Ising model is not.

Type
Research Article
Information
The ANZIAM Journal , Volume 19 , Issue 4 , December 1976 , pp. 387 - 399
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Lieb, E. and Robinson, D. W., Commun. Math. Phys. 28, 251 (1972).CrossRefGoogle Scholar
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[3]Robinson, D. W., Commun. Math. Phys. 7, 337 (1968).CrossRefGoogle Scholar
[4]Ruelle, D., Statistical Mechanics, Benjamin (New York) 1969.Google Scholar
[5]Streaer, R. F. and Wightman, A. S.: TCP, Spin and Statistics, and all that, Benjamin (New York) 1964.Google Scholar