Universal short-time quantum critical dynamics in imaginary time

Abstract

We propose a scaling theory for the universal imaginary-time quantum critical dynamics for both short times and long times. We discover that there exists a universal critical initial slip related to a small initial order parameter $M_0$. In this stage, the order parameter $M$ increases with the imaginary time $\tau$ as $M\propto M_0\tau^\theta$ with a universal initial slip exponent $\theta$. For the one-dimensional transverse-field Ising model, we estimate $\theta$ to be $0.373$, which is markedly distinct from its classical counterpart. Apart from the local order parameter, we also show that the entanglement entropy exhibits universal behavior in the short-time region. As the critical exponents in the early stage and in equilibrium are identical, we apply the short-time dynamics method to determine quantum critical properties. The method is generally applicable in both the Landau-Ginzburg-Wilson paradigm and topological phase transitions.