Correlated quantum percolation in the lowest Landau level

Our understanding of localization in the integer quantum Hall effect is informed by a combination of semi-classical models and percolation theory. Motivated by the effect of correlations on classical percolation we study numerically electron localization in the lowest Landau level in the presence of a power-law correlated disorder potential. Careful comparisons between classical and quantum dynamics suggest that the extended Harris criterion is applicable in the quantum case. This leads to a prediction of new localization quantum critical points in integer quantum Hall systems with power-law correlated disorder potentials. We demonstrate the stability of these critical points to addition of competing short-range disorder potentials, and discuss possible experimental realizations.Comment: 15 pages, 12 figure

An integrable modification of the critical Chalker-Coddington network model

We consider the Chalker-Coddington network model for the Integer Quantum Hall Effect, and examine the possibility of solving it exactly. In the supersymmetric path integral framework, we introduce a truncation procedure, leading to a series of well-defined two-dimensional loop models, with two loop flavours. In the phase diagram of the first-order truncated model, we identify four integrable branches related to the dilute Birman-Wenzl-Murakami braid-monoid algebra, and parameterised by the loop fugacity $n$. In the continuum limit, two of these branches (1,2) are described by a pair of decoupled copies of a Coulomb-Gas theory, whereas the other two branches (3,4) couple the two loop flavours, and relate to an $SU(2)_r \times SU(2)_r / SU(2)_{2r}$ Wess-Zumino-Witten (WZW) coset model for the particular values $n= -2\cos[\pi/(r+2)]$ where $r$ is a positive integer. The truncated Chalker-Coddington model is the $n=0$ point of branch 4. By numerical diagonalisation, we find that its universality class is neither an analytic continuation of the WZW coset, nor the universality class of the original Chalker-Coddington model. It constitutes rather an integrable, critical approximation to the latter.Comment: 34 pages, 18 figures, 3 appendice

A New Spin-Orbit Induced Universality Class in the Quantum Hall Regime ?

Using heuristic arguments and numerical simulations it is argued that the critical exponent $\nu$ describing the localization length divergence at the quantum Hall transition is modified in the presence of spin-orbit scattering with short range correlations. The exponent is very close to $\nu=4/3$, the percolation correlation length exponent, the prediction of a semi-classical argument. In addition, a region of weakly localized regime, where the localization length is exponentially large, is conjectured.Comment: 4 two-column pages including 4 eps figure

Scaling Properties of Conductance at Integer Quantum Hall Plateau Transitions

We investigate the scaling properties of zero temperature conductances at integer quantum Hall plateau transitions in the lowest Landau band of a two-dimensional tight-binding model. Scaling is obeyed for all energy and system sizes with critical exponent nu =7/3 . The arithmetic average of the conductance at the localization-delocalization critical point is found to be _c = 0.506 e^2 / h, in agreement with the universal longitudinal conductance predicted by an analytical theory. The probability distribution of the conductance at the critical point is broad with a dip at small G.Comment: 4 pages, 3 postscript figures, Submitted to PR

Connecting polymers to the quantum Hall plateau transition

A mapping is developed between the quantum Hall plateau transition and two-dimensional self-interacting lattice polymers. This mapping is exact in the classical percolation limit of the plateau transition, and diffusive behavior at the critical energy is shown to be related to the critical exponents of a class of chiral polymers at the $\theta$-point. The exact critical exponents of the chiral polymer model on the honeycomb lattice are found, verifying that this model is in the same universality class as a previously solved model of polymers on the Manhattan lattice. The mapping is obtained by averaging analytically over the local random potentials in a previously studied lattice model for the classical plateau transition. This average generates a weight on chiral polymers associated with the classical localization length exponent $\nu = 4/3$. We discuss the differences between the classical and quantum transitions in the context of polymer models and use numerical results on higher-moment scaling laws at the quantum transition to constrain possible polymer descriptions. Some properties of the polymer models are verified by transfer matrix and Monte Carlo studies.Comment: 9 pages, 2 figure

Quantum Hall Effect in Three Dimensional Layered Systems

Using a mapping of a layered three-dimensional system with significant inter-layer tunneling onto a spin-Hamiltonian, the phase diagram in the strong magnetic field limit is obtained in the semi-classical approximation. This phase diagram, which exhibit a metallic phase for a finite range of energies and magnetic fields, and the calculated associated critical exponent, $\nu=4/3$, agree excellently with existing numerical calculations. The implication of this work for the quantum Hall effect in three dimensions is discussed.Comment: 4 pages + 4 figure

Anderson Transitions

The physics of Anderson transitions between localized and metallic phases in disordered systems is reviewed. The term ``Anderson transition'' is understood in a broad sense, including both metal-insulator transitions and quantum-Hall-type transitions between phases with localized states. The emphasis is put on recent developments, which include: multifractality of critical wave functions, criticality in the power-law random banded matrix model, symmetry classification of disordered electronic systems, mechanisms of criticality in quasi-one-dimensional and two-dimensional systems and survey of corresponding critical theories, network models, and random Dirac Hamiltonians. Analytical approaches are complemented by advanced numerical simulations.Comment: 63 pages, 39 figures, submitted to Rev. Mod. Phy

Gauge Invariance and the Critical Properties of Quantum Hall Plateaux Transitions

A model consisting of a single massless scalar field with a topological coupling to a pure gauge field is defined and studied. It possesses an SL(2,Z) symmetry as a consequence of the gauge invariance. We propose that by adding impurities the model can be used to describe transitions between Quantum Hall plateaux. This leads to a correlation length exponent of 20/9, in excellent agreement with the most recent experimental measurements.Comment: 25 pages, minor changes in data discussion, Section V on connection with staircase model is expanded References added. Interpretive comments added in section 3 about the critical condition. with improved terminolog

Investigation of Terahertz Vibration–Rotation Tunneling Spectra for the Water Octamer

We report a combined theoretical and experimental study of the water octamer-h16. The calculations used the ring-polymer instanton method to compute tunnelling paths and splittings in full dimensionality. The experiments measured extensive high resolution spectra near 1.4 THz, for which isotope dilution experiments and group theoretical analysis support assignment to the octamer. Transitions appear as singlets, consistent with the instanton paths, which involve the breakage of two hydrogen-bonds and thus give tunneling splittings below experimental resolution