The finite group velocity of quantum spin systems (original) (raw)

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, and_A, B_ local observables, then \mathop {\lim }\limits_{\begin{array}{*{20}c} {|t| \to \infty } \\ {|x| > \upsilon |t|} \\ \end{array} } ||[\tau _t^\Phi \tau _x (A),B]||e^{\mu (\upsilon )t} = 0$$

whenever_v_ 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.

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References

  1. Robinson, D. W.: Commun. math. Phys.6, 151 (1967).
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  2. 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).
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Authors and Affiliations

  1. Dept. of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA
    Elliott H. Lieb
  2. Dept. of Physics, Univ. Aix-Marseille II, Marseille-Luminy, France
    Derek W. Robinson
  3. Centre de Physique Théorique C.N.R.S., 31, chemin J. Aiguier, F-13, Marseille 9°, France
    Derek W. Robinson

Authors

  1. Elliott H. Lieb
  2. Derek W. Robinson

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.

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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

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