Universality in the decay and evival of Loschmidt Echoes

Understanding non-equilbrium quench dynamics through a quantum phase transition is an important theoretical task. It has long been obsereved that a sudden quench dynamics near a quantum phase transition characterised by the Loschmidt echo exhibits a critically enhanced decay. In this contribution, we present the dynamical scaling laws that govern the decay and revival of the Loschmidt echo completely characgterised by equilibrium critical exponents of a critical point. We reveal such dynamical scaling laws by analyzing relevant perturbations to the Loschmidt echo cast in a scaling invariant form. We will show the validity and the generality of the predicted dynamical scaling laws using numerical calculation of a diverse range of critical models such as Ising spin models with a short and long range interaction, a finite-component system phase transition, and a topological phase transition. Our finding promotes the Loschmidt echo to a quantitative non-equilibrium probe of criticality and allows for quantitative predictions on the role of criticality on various physical scenarios where the Loschmidt echo is central to describing non-equilibrium dynamics.