22 research outputs found
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 . 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 Wess-Zumino-Witten (WZW) coset model for the particular values where is a positive integer. The truncated
Chalker-Coddington model is the 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 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 , 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 -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 . 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,
, 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