Probing scale-invariant prethermal regime in systems quenched to criticality

An experimentally feasible way to probe quantum phase transitions is through dynamical measurements where one quenches to the close vicinity of a quantum critical point (QCP). Upon quenching to a QCP, quantum many-body systems exhibit a prethermal temporal regime in one-point observables. Here we present an analytical framework for the transverse field Ising chain (TFIC) that leads us to a scale-invariant and universal scaling function of this critically prethermal regime both in edge and bulk observables. Our work provides a quantitative definition of critical slowing down of system observables, due to the quantum phase transition, in far from equilibrium setting. It further explains the robustness behind the nonequilibrium exponents that are numerically extracted for the spatially minimal and dynamical order parameters of TFIC.