The finite group velocity of quantum spin systems

  title={The finite group velocity of quantum spin systems},
  author={Elliott H. Lieb and Derek W. Robinson},
  journal={Communications in Mathematical Physics},
AbstractIt is shown that if Φ is a finite range interaction of a quantum spin system,τtΦ the associated group of time translations, τx 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… 

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