Quantum Transition Between Magnetically Ordered and Mott Glass Phases

Abstract

We discuss a quantum transition from a superfluid to a Mott glass phases in disordered Bosesystems by the example of an isotropic spin-1 2 antiferromagnet with spatial dimension d ≥ 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 − β/ν for the dynamical critical exponent and φ = zν, 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.PACS numbers: 64.70. Tg, 72.15.Rn, 74.40.Kb I. INTRODUCTIONThe interplay of quantum fluctuations and quenched disorder leads to a variety of unconventional phenomena and special quantum phases which are of great current interest. 1-5 Examples include metal-insulator and superconductorinsulator transitions, heavy-fermion systems, interacting bosons in disordered potential (the so-called dirty bosons), and doped quantum magnets. In the present paper, we discuss effects of disorder on a quantum phase transition (QPT) between a Néel and a dimerized singlet phases in an isotropic quantum spin-1 2 Heisenberg antiferromagnet (HAF) with spatial dimension d ≥ 2 and with tunable spin couplings. Our conclusions should be relevant to various Bose-systems from the same universality class.The Hamiltonian of the model we discuss has the formwhere i, j denote nearest-neighbor sites of a hypercubic d-dimensional lattice. A three-dimensional version of model (1) without disorder is shown in Fig. 1, where thin and bold lines denote spin couplings with exchange constants J > 0 and gJ > 0, respectively. Decreasing g beyond a critical value g c drives the system through a QPT from the dimerized phase to the Néel one. In pure magnets, such transition is described by O(3) nonlinear quantum field theory and characterized by the dynamical critical exponent z = 1 at d ≥ 1. 3 It has attracted much attention in recent years (see, e.g., Refs. 6-10 and references therein). This interest is stimulated by experimental observation of pressure-induced transitions of this kind in TlCuCl 3 , 11-13 KCuCl 3 , 14,15 CsFeCl 3 , 16 and (C 4 H 12 N 2 )Cu 2 Cl 6 17 . In these compounds, the applied pressure changes exchange coupling constants so that the transition occurs at some pressure value.Another way to bring system (1) from the dimerized to a magnetically ordered phase is to apply a magnetic field h. It is well known that a canted antiferromagnetic order arises in a field range h c1 < h < h c2 and all spins are parallel to the mag...

Quantum transitions from superfluid to insulating phases in disordered Bose systems

“…It was shown in Refs. 29,30 that results obtained by this approach are consistent with the scaling theory proposed in Ref. 1 for the description of the SF-BG transition.…”

“…On smaller length scale, excitations (the so-called "fractons") are expected to be localized as in diluted HAFs. 1,29,30,32 Quantities introduced above scale near g c as…”

“…21,[26][27][28] ) that transitions from the ordered to glassy phases mentioned above resemble the percolation transition: the ordered part of the system having the form of an infinite network breaks up into domains upon approaching the QPT which are surrounded by disordered regions (see also Refs. 29,30 for extra discussion). Then, main ideas of the theory of collinear magnets on depleted lattices near the percolation threshold [31][32][33][34][35] were used in Refs.…”

“…Then, main ideas of the theory of collinear magnets on depleted lattices near the percolation threshold [31][32][33][34][35] were used in Refs. 29,30 to describe SF-BG and SF-MG transitions at d ≥ 2. Those considerations were based on the hydrodynamic description of the long-wavelength spin excitations and on the assumption that the magnetically ordered part of the system shows self-similar (fractal) properties.…”

“…1 for d ≥ 2 (only the inequality 2 − 2d < η ≤ 2 − z was suggested which is valid for all d ≥ 1) and they were also omitted in Ref. 30 in the consideration of the SF-MG transition. We discuss our general findings in Sec.…”