J. T. Chalker

Percolation, quantum tunnelling and the integer Hall effect

A model is introduced for Anderson localisation in the integer quantum Hall regime. The model represents a system with a disordered potential that varies slowly on the scale of the magnetic length, but includes quantum tunnelling and interference effects. Numerical calculations indicate that the localisation length diverges only at the centre of each Landau band. The scaling behaviour near the mobility edge is analysed: results suggest that quantum tunnelling induces crossover at the classical percolation threshold to critical behaviour similar to that found previously for a rapidly varying potential.

Exact results for interacting electrons in high Landau levels

We study a two-dimensional electron system in a magnetic field with a fermion hard-core interaction and without disorder. Projecting the Hamiltonian onto the {ital n}th Landau level, we show that the Hartree-Fock theory is exact in the limit {ital n}{r_arrow}{infinity}, for the high-temperature, uniform density phase of an infinite system; for a finite-size system, it is exact at all temperatures. In addition, we show that a charge-density wave arises below a transition temperature {ital T}{sub {ital t}}. Using Landau theory, we construct a phase diagram which contains both unidirectional and triangular charge-density wave phases. We discuss the unidirectional charge-density wave at zero temperature and argue that quantum fluctuations are unimportant in the large-{ital n} limit. Finally, we discuss the accuracy of the Hartree-Fock approximation for potentials with a nonzero range such as the Coulomb interaction. {copyright} {ital 1996 The American Physical Society.}

Properties of a Classical Spin Liquid: The Heisenberg Pyrochlore Antiferromagnet

We study the low-temperature behavior of the classical Heisenberg antiferromagnet with nearest neighbor interactions on the pyrochlore lattice. Because of geometrical frustration, the ground state of this model has an extensive number of degrees of freedom. We show, by analyzing the effects of small fluctuations around the ground-state manifold, and from the results of Monte Carlo and molecular dynamics simulations, that the system is disordered at all temperatures T and has a finite relaxation time, which varies as

LOW-TEMPERATURE PROPERTIES OF CLASSICAL GEOMETRICALLY FRUSTRATED ANTIFERROMAGNETS

{T}^{\ensuremath{-}1}

Dynamics of a Two-Dimensional Quantum Spin Liquid: Signatures of Emergent Majorana Fermions and Fluxes

for small T.

Three-dimensional disordered conductors in a strong magnetic field: Surface states and quantum Hall plateaus.

We study the ground-state and low-energy properties of classical vector spin models with nearest-neighbor antiferromagnetic interactions on a class of geometrically frustrated lattices, which includes the kagome and pyrochlore lattices. We explore the behavior of these magnets that results from their large ground-state degeneracies, emphasizing universal features and systematic differences between individual models. We investigate the circumstances under which thermal fluctuations select a particular subset of the ground states, and find that this happens only for the models with the smallest ground-state degeneracies. For the pyrochlore magnets, we give an explicit construction of all ground states, and show that they are not separated by internal energy barriers. We study the precessional spin dynamics of the Heisenberg pyrochlore antiferromagnet. There is no freezing transition or selection of preferred states. Instead, the relaxation time at low temperature T is of order

Scaling and eigenfunction correlations near a mobility edge

\ensuremath{\Elzxh}{/k}_{B}T.

Unified model for two localization problems: Electron states in spin-degenerate Landau levels and in a random magnetic field.

We argue that this behavior can also be expected in some other systems, including the Heisenberg model for the compound

Random Walks through the Ensemble: Linking Spectral Statistics with Wave-Function Correlations in Disordered Metals.

{\mathrm{SrCr}}_{8}{\mathrm{Ga}}_{4}{\mathrm{O}}_{19}.