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In non-relativistic quantum theories with short-range Hamiltonians, a velocity $v$ can be chosen such that the influence of any local perturbation is approximately confined to within a distance $r$ until a time $t \sim r/v$, thereby defining a linear light cone and giving rise to an emergent notion of locality.
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The results presented are significantly more general than Eq. ( 1
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( S \rm{S} ee S \rm{S} upplemental M \rm{M} aterial at link xxx \rm{xxx} for details omitted in the main text)
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As α \alpha gets larger, larger separations are required for the algebraic decay to dominate over the exponential decay. Strictly speaking, this consideration imposes that Eq. ( 19
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Z.-X. Gong, M. Foss-Feig, C. W. Clark, and A. V. Gorshkov, (in preparation) (2014b)
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