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Quantum Critical Dynamics Simulation of Dirty Boson Systems

Recently the scaling result $z=d$ for the dynamic critical exponent at the Bose glass to superfluid quantum phase transition has been questioned both on theoretical and numerical grounds. This motivates a careful evaluation of the critical exponents in order to determine the actual value of $z$. We study a model of quantum bosons at T=0 with disorder in 2D using highly effective worm Monte Carlo simulations. Our data analysis is based on a finite size scaling approach to determine the scaling of the quantum correlation time from simulation data for boson world lines. The resulting critical exponents are $z=1.8 \pm 0.05, ν=1.15 \pm 0.03,$ and $η=-0.3 \pm 0.1$, hence suggesting that $z=2$ is not satisfied.