In non-relativistic quantum theories the Lieb-Robinson bound defines
an effective light cone with exponentially small tails outside of it. In
this work we use it to derive a bound for the correlation function of
two local disjoint observables at different times if the initial state
has a power-law decay. We show that the exponent of the power-law of the
bound is identical to the initial (equilibrium) decay. We explicitly
verify this result by studying the full dynamics of the susceptibilities
and correlations in the exactly solvable Luttinger model after a sudden
quench from the non-interacting to the interacting model.
Spin Hall insulators beyond the helical Luttinger model
