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arXiv:cond-mat/9811047 · Physical Review Letters

Spin Bose-Glass Phase in Bilayer Quantum Hall Systems at ν=2

Eugene Demler, S. Das Sarma

Published May 10, 1999• 48 citations
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Abstract

We develop an effective spin theory to describe magnetic properties of the $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ quantum Hall bilayer systems. In the absence of disorder this theory agrees with the microscopic Hartree-Fock calculations, and for finite disorder it predicts the existence of a novel spin Bose-glass phase. The Bose glass is characterized by the presence of domains of canted antiferromagnetic phase with zero average antiferromagnetic order and short range correlations. It has infinite antiferromagnetic transverse susceptibility and finite longitudinal spin susceptibility. Transition from the canted antiferromagnetic phase to the spin Bose-glass phase is characterized by a universal value of the spin conductance.

DOI
10.1103/physrevlett.82.3895

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We develop an effective spin theory to describe magnetic properties of the \ensuremathν=2\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2\ensuremathν=2 quantum Hall bilayer systems. In the absence of disorder this theory agrees with the microscopic Hartree-Fock calculations, and for finite disorder it predicts the existence of a novel spin Bose-glass phase. The Bose glass is characterized by the presence of domains of canted antiferromagnetic phase with zero average antiferromagnetic order and short range correlations. It has infinite antiferromagnetic transverse susceptibility and finite longitudinal spin susceptibility. Transition from the canted antiferromagnetic phase to the spin Bose-glass phase is characterized by a universal value of the spin conductance.
We present details of earlier studies [Zheng et al., Phys. Rev. Lett. 78, 310 (1997) and Das Sarma et al., 79, 917 (1997)] and additional results on double-layer quantum Hall systems at a total filling $\ensuremath{\nu}=2{\ensuremath{\nu}}_{1}$, where a single layer at filling ${\ensuremath{\nu}}_{1}$ forms a ferromagnetic, fully spin-polarized, gapped incompressible quantum Hall state. For the case ${\ensuremath{\nu}}_{1}=1$, a detailed Hartree-Fock analysis is carried out on a realistic, microscopic Hamiltonian. Apart from the state continuously connected to the ground state of two well-separated layers, we find two double-layer quantum Hall phases: one with a finite interlayer antiferromagnetic spin ordering in the plane orthogonal to the applied field (the ``canted'' state), and the other a spin singlet. The quantum transitions between the various quantum Hall states are continuous, and are signaled by the softening of collective intersubband spin-density excitations. For the case of general ${\ensuremath{\nu}}_{1}$, closely related results are obtained by a semi-phenomenological continuum quantum field theory description of the low-lying spin excitations using a nonlinear $\ensuremath{\sigma}$ model. Because of its broken symmetry, the canted phase supports a linearly dispersing Goldstone mode and has a finite-temperature Kosterlitz-Thouless transition. We present results on the form of the phase diagram, the magnitude of the canted order parameter, the collective excitation dispersions, the specific heat, the form of the dynamic light-scattering spectrum at finite temperature, and the Kosterlitz-Thouless critical temperature. Our findings are consistent with recent experimental results.
We study quantum phase transitions of Mott insulators between spin-glass and featureless paramagnetic phases. Specifically, we consider a triangular-lattice bilayer Heisenberg model with bond disorder. The clean system has two phases, a dimer quantum paramagnet and a non-collinear antiferromagnet, separated by a quantum critical point. Bond disorder destroys the antiferromagnetic phase via the interference of dipolar textures and results in spin-glass order, such that the system features a quantum phase transition between spin-glass and dimer phases. We study the vicinity of this transition using a variant of bond-operator theory and calculate thermodynamic observables as well as excitation spectra. Bond disorder leads to strong inhomogeneities near the transition which suppresses non-collinearities and leads to anomalously weak glassiness in the near-critical quantum spin glass. We characterize the low-energy excitations which have a strong tendency towards spatial localization, and we track the behavior of the amplitude (i.e. Higgs) mode across the glass phase whose spectral weight we find to be strongly suppressed due to interference effects.
We study intersubband spin density collective modes in double-layer quantum Hall systems at $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ within the time-dependent Hartree-Fock approximation. We find that these intersubband spin density excitations may soften under experimentally accessible conditions, signaling a phase transition to a new quantum Hall state with interlayer inplane antiferromagnetic spin correlations. We show that this novel canted antiferromagnetic phase is energetically stable and that the phase transition is continuous.
We study the quantum transition at T=0 in the spin-1/2 Ising spin glass in a transverse field in two dimensions. The world line path integral representation of this model corresponds to an effective classical system in 2+1 dimensions, which we study by Monte Carlo simulations. Values of the critical exponents are estimated by a finite-size scaling analysis. We find that the dynamical exponent, z, and the correlation length exponent, \ensuremath{\nu}, are given by z=1.5\ifmmode\pm\else\textpm\fi{}0.05 and \ensuremath{\nu}=1.0\ifmmode\pm\else\textpm\fi{}0.1. Both the linear and nonlinear susceptibility are found to diverge at the critical point.
We examine the effects of disorder on dimerized quantum antiferromagnets in a magnetic field, using the mapping to a lattice gas of hard-core bosons with finite-range interactions. Combining a strong-coupling expansion, the replica method, and a one-loop renormalization-group analysis, we investigate the nature of the glass phases formed. We find that away from the tips of the Mott lobes, the transition is from a Mott insulator to a compressible Bose glass, however the compressibility at the tips is strongly suppressed. We identify this finding with the presence of a rare Mott glass phase and demonstrate that the inclusion of replica symmetry breaking is vital to correctly describe the glassy phases. This result suggests that the formation of Bose and Mott glass phases is not simply a weak localization phenomenon but is indicative of much richer physics. We discuss our results in the context of both ultracold atomic gases and spin-dimer materials.