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arXiv:1701.08624 · Annalen der Physik

Quantum Transition Between Magnetically Ordered and Mott Glass Phases

A. V. Syromyatnikov

Published Jul 31, 2017• 2 citations
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Abstract

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‐ antiferromagnet with spatial dimension 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 for the dynamical critical exponent and , where ϕ, β, and ν 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.

DOI
10.1002/andp.201700055

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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‐ antiferromagnet with spatial dimension 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 for the dynamical critical exponent and , where ϕ, β, and ν 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.
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