Universal Scaling in Fast Quenches Near Lifshitz-Like Fixed Points

We study critical dynamics through time evolution of quantum field theories driven to a Lifshitz-like fixed point, with $z>1$, under relevant deformations. The deformations we consider are fast smooth quantum quenches, namely when the quench scale $\delta t^{-z}$ is large compared to the deformation scale. We show that in holographic models the response of the system merely depends on the scaling dimension of the quenched operator as $\delta\lambda\cdot\delta t^{d-2\Delta+z-1}$, where $\delta\lambda$ is the deformation amplitude. This scaling behavior is enhanced logarithmically in certain cases. We also study free Lifshitz scalar theory deformed by mass operator and show that the universal scaling of the response completely matches with holographic analysis. We argue that this scaling behavior is universal for any relevant deformation around Lifshitz-like UV fixed points.