Universal short time quantum critical dynamics of finite size systems

We investigate the short time quantum critical dynamics in the imaginary time relaxation processes of finite size systems. Universal scaling behaviors exist in the imaginary time evolution and in particular, the system undergoes a critical initial slip stage characterized by an exponent θ. We apply the method to the one- and two-dimensional transverse field Ising models using quantum Monte Carlo simulations. In the one-dimensional case, we locate the quantum critical point at (h/J)c=1.00003(8), and estimate the critical initial slip exponent θ=0.3734(2), static exponents β/ν=0.1250(2). For the two-dimensional square-lattice system, the critical coupling ratio is given by 3.04451(7) while the critical exponents are θ=0.209(3) and β/ν=0.5227(4). Remarkably, the critical initial slip exponents obtained in both models are notably distinct from their classical counterparts, owing to the essential differences between classical and quantum dynamics. The short time critical dynamics and the imaginary time relaxation QMC approach can be readily adapted to various models. Reference: Phys. Rev. B 96, 094304 (2017).