, Volume 28, Issue 3, pp 251-257

The finite group velocity of quantum spin systems

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

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.