Correlation functions in the prethermalized regime after a quantum quench of a spin-chain

Results are presented for a two-point correlation function of a spin-chain after a quantum quench for an intermediate time regime where inelastic effects are weak. A Callan-Symanzik like equation for the correlation function is explicitly constructed which is used to show the appearance of three distinct scaling regimes. One is for spatial separations within a light-cone, the second is for spatial separations on the light-cone, and the third is for spatial separations outside the light-cone. In these three regimes, the correlation function is found to decay with power-laws with nonequilibrium exponents that differ from those in equilibrium, as well as from those obtained from quenches in a quadratic Luttinger liquid theory. A detailed discussion is presented on how the existence of scaling depends on the properties of the initial state before the quench.