Quantum Critical Dynamics Simulation of Dirty Boson Systems

TL;DR

This study uses advanced Monte Carlo simulations to accurately determine the critical exponents of disordered 2D boson systems at zero temperature, challenging the previously assumed dynamic critical exponent value of 2.

Contribution

The paper provides a precise numerical evaluation of critical exponents in disordered 2D boson systems, questioning the traditional $z=d$ scaling hypothesis.

Findings

Critical exponent z ≈ 1.8, not 2

Correlation length exponent ν ≈ 1.15

Anomalous dimension η ≈ -0.3

Abstract

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 $z=1.8 \pm 0.05, \nu=1.15 \pm 0.03,$ and $\eta=-0.3 \pm 0.1$, hence suggesting that $z=2$ is not satisfied.