Quantum transition between magnetically ordered and Mott glass phases

We discuss a quantum transition from a superfluid to a Mott glass phases in disordered Bose-systems by the example of an isotropic spin-$\frac{1}{2}$ antiferromagnet with spatial dimension $d\ge 2$ and with disorder in tunable exchange couplings. Our analytical consideration is based on general properties of a system in critical regime, on the assumption that the magnetically order part of the system shows fractal properties near the transition, and on a hydrodynamic description of long-wavelength magnons in the magnetically ordered (“superfluide”) phase. Our results are fully consistent with a scaling theory based on an ansatz for the free energy proposed by M.P. Fisher et al. (Phys. Rev. B 40, 546 (1989)). We obtain $z=d-\beta \mathrm{/}\nu$ for the dynamical critical exponent and $\varphi =z\nu$, where $\varphi$, $\beta$, and $\nu$ are critical exponents of the critical temperature, the order parameter, and the correlation length, respectively. The density of states of localized excitations (fractons) is found to show a superuniversal (i.e., independent of $d$) behavior.