Universal critical dynamics of quantum geometry

Abstract: In this study, we prove that the quantum critical point in the ground state of quantum many-body systems, can also govern the universal dynamical behavior when the systems are driven far from equilibrium, which can be captured by the evolution of the quantum geometry of the systems. By investigating quantum quench dynamics in quadratic fermionic models, we prove that the quantum volume of these systems typically grows linearly over time, with a growth velocity demonstrating universal behavior: its first derivative over the control parameter exhibits a discontinuity at the quantum critical point, with an universal jump value that is independent of specific models, but is crucially determined by the system dimension. This result reveals universal dynamical properties of non-equilibrium quantum many-body systems