Abstract
It is shown that if Φ is a finite range interaction of a quantum spin system,τ t Φ the associated group of time translations, τ x the group of space translations, andA, B local observables, then
wheneverv is sufficiently large (v>VΦ) where μ(v)>0. The physical content of the statement is that information can propagate in the system only with a finite group velocity.
Similar content being viewed by others
References
Robinson, D. W.: Commun. math. Phys.6, 151 (1967).
Robinson, D. W.: Commun. math. Phys.7, 337 (1968). -- See also; Streater, R. F.: Commun. math. Phys.7, 93 (1968). -- Ruskai, M. B.: Commun. math. Phys.20, 193 (1971).
Author information
Authors and Affiliations
Additional information
Work supported by National Science Foundation Grant N°: GP-31674 X.
Work supported by National Science Foundation Grants N°: GP-31239 X and GP-30819 X.
Rights and permissions
About this article
Cite this article
Lieb, E.H., Robinson, D.W. The finite group velocity of quantum spin systems. Commun.Math. Phys. 28, 251–257 (1972). https://doi.org/10.1007/BF01645779
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01645779