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 implicit assumptions of the numerical value of z, in contrast to most prior studies. 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 >= 2/d as well as a value of z significantly larger than previous studies, and for the quantum rotor model consistent with z = d.