Quantum Critical Scaling of Dirty Bosons in Two Dimensions

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$\eta=-0.3(1)$withacriticalhoppingparameterof$t_c=0.0760(5)$. In both cases do we find a correlation length exponent consistent with $\nu =1$, saturating the bound $\nu \ge 2\mathrm{/}d$ as well as a value of $z$ significantly larger than previous studies, and for the quantum rotor model consistent with $z=d$.