Aging dynamics in quenched noisy long-range quantum Ising models

We consider the d-dimensional transverse-field Ising model with power-law interactions J/r(d+sigma) in the presence of a noisy longitudinal field with zero average. We study the longitudinal-magnetization dynamics of an initial paramagnetic state after a sudden switch-on of both the interactions and the noisy field. While the system eventually relaxes to an infinite-temperature state with vanishing magnetization correlations, we find that two-time correlation functions show aging at intermediate times. Moreover, for times shorter than the inverse noise strength kappa and distances longer than a(J/kappa)(2/sigma) with a being the lattice spacing, we find a critical scaling regime of correlation and response functions consistent with the model A dynamical universality class with an initial-slip exponent theta = 1 and dynamical critical exponent z = sigma/2. We obtain our results analytically by deriving an effective action for the magnetization field including the noise in a nonperturbative way. The above scaling regime is governed by a nonequilibrium fixed point dominated by the noise fluctuations