Universal short-time quantum critical dynamics
Shuai Yin1,2*, Peizhi Mai3,2, Shuyi Zhang2,4, Fan Zhong2
1Department of physics, National Tsinghua university, Hsinchu, Taiwan
2State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics and Engineering, Sun Yat-sen university, Guangzhou, China
3Physics Department, University of California, Santa Cruz, United States of America
4Perimeter Institute for Theoretical Physics, Perimeter Institute, Canada
* presenting author:陰 Yin帥 Shuai, email:sysuyinshuai@gmail.com
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~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.

Keywords: quantum phase transition, nonequilibrium quantum criticality, short-time dynamics