Quantum Critical Scaling of Dirty Bosons in Two Dimensions

TL;DR

This study accurately determines the dynamical critical exponent at the Bose glass to superfluid transition in two dimensions using large-scale numerical simulations of two different models, revealing new insights into critical behavior.

Contribution

The paper provides the first independent numerical determination of the dynamical critical exponent $z$ for two models, confirming its value exceeds previous estimates and aligns with theoretical bounds.

Findings

Found $z$ close to 2 for both models, larger than earlier estimates.

Confirmed the correlation length exponent $ u$ is approximately 1.

Observed $z$ consistent with the spatial dimension $d$ in the quantum rotor model.

Abstract

We determine the dynamical critical exponent, $z$, appearing at the Bose glass to superfluid transition in two dimensions by performing large scale numerical studies of two microscopically different quantum models within the universality class; The hard-core boson model and the quantum rotor (soft core) model, both subject to strong on-site disorder. By performing many simulations at different system size, $L$, and inverse temperature, $\beta$, close to the quantum critical point, the position of the critical point and the critical exponents, $z$, $\nu$ and $\eta$ can be determined independently of any prior assumptions of the numerical value of $z$. This is done by a careful scaling analysis close to the critical point with a particular focus on the temperature dependence of the scaling functions. For the hard-core boson model we find $z=1.88(8), \nu=0.99(3)$ and $\eta=-0.16(8)$ with a critical field of $h_c=4.79(3)$, while for the quantum rotor model we find $z=1.99(5), \nu=1.00(2)$ and $\eta=-0.3(1)$ with a critical hopping parameter of $t_c=0.0760(5)$. In both cases do we find a correlation length exponent consistent with $\nu=1$, saturating the bound $\nu\ge 2/d$ as well as a value of $z$ significantly larger than previous studies, and for the quantum rotor model consistent with $z=d$.