# Quantum transition between magnetically ordered and Mott glass phases

## TL;DR

This paper investigates a quantum phase transition between superfluid and Mott glass phases in disordered Bose systems, providing analytical insights into critical behavior, fractal properties, and excitation spectra.

## Contribution

It introduces a scaling theory for the transition, deriving critical exponents and demonstrating superuniversal behavior of localized excitations in disordered antiferromagnets.

## Key findings

- Derived the relation z=d−β/ν for the dynamical critical exponent
- Established the superuniversal behavior of fracton density of states
- Confirmed consistency with Fisher's scaling theory

## Abstract

We discuss a quantum transition from a superfluid to a Mott glass phases in disordered Bose-systems by the example of an isotropic spin-$\frac12$ antiferromagnet with spatial dimension $d\ge2$ 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 $z=d-\beta/\nu$ for the dynamical critical exponent and $\phi = z\nu$, where $\phi$, $\beta$, 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.