7 research outputs found
Symmetry Aspects and Finite-Size Scaling of Quantum Hall Fluids
The exactness and universality observed in the quantum Hall effect suggests
the existence of a symmetry principle underlying Laughlin's theory. We review
the role played by the infinite and conformal algebras as
dynamical symmetries of incompressible quantum fluids and show how they predict
universal finite-size effects in the excitation spectrum.Comment: 15 pages, CERN-TH-6784/93, LateX fil
Chiral Partition Functions of Quantum Hall Droplets
Chiral partition functions of conformal field theory describe the edge
excitations of isolated Hall droplets. They are characterized by an index
specifying the quasiparticle sector and transform among themselves by a
finite-dimensional representation of the modular group. The partition functions
are derived and used to describe electron transitions leading to Coulomb
blockade conductance peaks. We find the peak patterns for Abelian hierarchical
states and non-Abelian Read-Rezayi states, and compare them. Experimental
observation of these features can check the qualitative properties of the
conformal field theory description, such as the decomposition of the Hilbert
space into sectors, involving charged and neutral parts, and the fusion rules.Comment: 37 pages, 8 figure
Classification of Quantum Hall Universality Classes by $\ W_{1+\infty}\ $ symmetry
We show how two-dimensional incompressible quantum fluids and their
excitations can be viewed as edge conformal field theories,
thereby providing an algebraic characterization of incompressibility. The
Kac-Radul representation theory of the algebra leads then to
a purely algebraic complete classification of hierarchical quantum Hall states,
which encompasses all measured fractions. Spin-polarized electrons in
single-layer devices can only have Abelian anyon excitations.Comment: 11 pages, RevTeX 3.0, MPI-Ph/93-75 DFTT 65/9
Neutral modes edge state dynamics through quantum point contacts
Dynamics of neutral modes for fractional quantum Hall states is investigated
for a quantum point contact geometry in the weak-backscattering regime. The
effective field theory introduced by Fradkin-Lopez for edge states in the Jain
sequence is generalized to the case of propagating neutral modes. The dominant
tunnelling processes are identified also in the presence of non-universal
phenomena induced by interactions. The crossover regime in the backscattering
current between tunnelling of single-quasiparticles and of agglomerates of
p-quasiparticles is analysed. We demonstrate that higher order cumulants of the
backscattering current fluctuations are a unique resource to study
quantitatively the competition between different carrier charges. We find that
propagating neutral modes are a necessary ingredient in order to explain this
crossover phenomena.Comment: 28 pages, 5 figure