Recent experiments show that double layer quantum Hall systems may have a ground state with canted antiferromagnetic order. In the vicinity of a quantum critical point, the order vanishes at a temperature ${T}_{\mathrm{KT}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\kappa}H$, where
H is the magnetic field and $\ensuremath{\kappa}$ is a universal number. We present quantum Monte Carlo simulations on a model spin system which support the universality of $\ensuremath{\kappa}$ and determine its value. This allows experimental tests of an intrinsically quantum-mechanical universal quantity, which is not also a property of a higher dimensional classical critical point.
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.
A quantum system can undergo a continuous phase transition at the absolute zero of temperature as some parameter entering its Hamiltonian is varied. These transitions are particularly interesting for, in contrast to their classical finite-temperature counterparts, their dynamic and static critical behaviors are intimately intertwined. Considerable insight is gained by considering the path-integral description of the quantum statistical mechanics of such systems, which takes the form of the classical statistical mechanics of a system in which time appears as an extra dimension. In particular, this allows the deduction of scaling forms for the finite-temperature behavior, which turns out to be described by the theory of finite-size scaling. It also leads naturally to the notion of a temperature-dependent dephasing length that governs the crossover between quantum and classical fluctuations. Using these ideas, a scaling analysis of experiments on Josephson-junction arrays and quantum-Hall-effect systems is presented.
We study the spin quantum Hall effect and transitions between Hall plateaus in quasi-two-dimensional network models consisting of several coupled layers. Systems exhibiting the spin quantum Hall effect belong to class C in the symmetry classification for Anderson localization, and for network models in this class there is an established mapping between the quantum problem and a classical one involving random walks. This mapping permits numerical studies of plateau transitions in much larger samples than for other symmetry classes, and we use it to examine localization in systems consisting of
n weakly coupled layers. Standard scaling ideas lead one to expect
n distinct plateau transitions, but in the case of the unitary symmetry class this conclusion has been questioned. Focusing on a two-layer model, we demonstrate that there are two separate plateau transitions, with the same critical properties as in a single-layer model, even for very weak interlayer coupling.
A relation between the correlation entropy and the correlation functions for the general spin-1/2 systems is obtained. It is shown that the correlation entropy catches some characters of correlation behavior and can be used to quantify the quantum and finite-temperature phase transitions, including the infinite order or topological ones. As an example, the Kosterlitz–Thouless transition in the quantum two-dimensional XY model is investigated. The critical temperature and the critical exponents are determined from the finite-size scaling analysis of the correlation entropy.
We describe the nonzero temperature
(T), low frequency $(\ensuremath{\omega})$ dynamics of the order parameter near quantum critical points in two spatial dimensions
(d), with a special focus on the regime $\ensuremath{\Elzxh}\ensuremath{\omega}\ensuremath{\ll}{k}_{B}T$. For the case of a ``relativistic,''
O(n)-symmetric, bosonic quantum field theory we show that, for small $\ensuremath{\epsilon}=3\ensuremath{-}d$, the dynamics is described by an effective classical model of waves with a quartic interaction. We provide analytical and numerical analyses of the classical wave model directly in
d=2. We describe the crossover from the finite frequency, ``amplitude fluctuation,'' gapped quasiparticle mode in the quantum paramagnet (or Mott insulator), to the zero frequency ``phase''
(n> 2) or ``domain wall''
(n=1) relaxation mode near the ordered state. For static properties, we show how a surprising, duality-like transformation allows an exact treatment of the strong-coupling limit for all n. For
n=2, we compute the universal T dependence of the superfluid density below the Kosterlitz-Thouless temperature, and discuss implications for the high temperature superconductors. For
n=3, our computations of the dynamic structure factor relate to neutron scattering experiments on
La1.85Sr0.15CuO4, and to light scattering experiments on double layer quantum Hall systems. We expect that closely related effective classical wave models will apply also to other quantum critical points in
d=2. Although computations in appendixes do rely upon technical results on the $\ensuremath{\epsilon}$-expansion of quantum critical points obtained in earlier papers, the physical discussion in the body of the paper is self-contained, and can be read without consulting these earlier works.