Infinite symmetry in the quantum Hall effect

@article{Cappelli1993InfiniteSI,
  title={Infinite symmetry in the quantum Hall effect},
  author={Andrea Cappelli and Carlo A. Trugenberger and Guillermo R. Zemba},
  journal={Nuclear Physics},
  year={1993},
  volume={396},
  pages={465-490}
}
Abstract Free planar electrons in a uniform magnetic field are shown to possess the dynamical symmetry of area-preserving diffeomorphisms (W-infinity algebra). Intuitively, this is a consequence of gauge invariance, which forces dynamics to depend only on the flux. The infinity of generators of this symmetry act within each Landau level, which is infinite dimensional in the thermodynamic limit. The incompressible ground states corresponding to completely filled Landau levels (integer quantum… 
Conformal symmetry and universal properties of quantum Hall states
Abstract The low-lying excitations of a quantum Hall state on a disk geometry are edge excitations. Their dynamics is governed by a conformal field theory on the cylinder defined by the disk boundary
Modular invariant partition functions in the quantum Hall effect
Abstract We study the partition function for the low-energy edge excitations of the incompressible electron fluid. On an annular geometry, these excitations have opposite chiralities on the two
Infinite Symmetry in the Fractional Quantum Hall Effect
We have generalized recent results on the integer quantum Hall effect, constructing explicitly a W1+ infinity for the fractional quantum Hall effect such that the negative modes annihilate the
Large N limit in the quantum Hall effect
Abstract The Laughlin states for N interacting electrons at the plateaus of the fractional Hall effect are studied in the thermodynamic limit of large N . It is shown that this limit leads to the
Extended dynamical symmetries of Landau levels in higher dimensions
Continuum models for time-reversal (TR) invariant topological insulators (Tis) in d ≥ 3 dimensions are provided by harmonic oscillators coupled to certain SO( d ) gauge fields. These models are
Duality and the fractional quantum Hall effect
Abstract The edge states of a sample displaying the quantum Hall effect (QHE) can be described by a (1+1)-dimensional (conformal) field theory of d massless scalar fields taking values on a d
Bulk-boundary correspondence in the quantum Hall effect
We present a detailed microscopic study of edge excitations for n filled Landau levels. We show that the higher-level wavefunctions possess a non-trivial radial dependence that should be integrated
2D superconductivity: Classification of universality classes by infinite symmetry
Abstract I consider superconducting condensates which become incompressible in the infinite gap limit. Classical 2D incompressible fluids possess the dynamical symmetry of area-preserving
Geometric Model of Topological Insulators from the Maxwell Algebra
We propose a novel geometric model of three-dimensional topological insulators in presence of an external electromagnetic field. The gapped boundary of these systems supports relativistic quantum
Integrable quantum hydrodynamics in two-dimensional phase space
Quantum liquids in two dimensions represent interesting dynamical quantum systems for several reasons, among them the possibility of the existence of infinite hidden symmetries, such as conformal
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 64 REFERENCES
Conformal symmetry and universal properties of quantum Hall states
Abstract The low-lying excitations of a quantum Hall state on a disk geometry are edge excitations. Their dynamics is governed by a conformal field theory on the cylinder defined by the disk boundary
Large N limit in the quantum Hall effect
Abstract The Laughlin states for N interacting electrons at the plateaus of the fractional Hall effect are studied in the thermodynamic limit of large N . It is shown that this limit leads to the
Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory - Nucl. Phys. B241, 333 (1984)
We present an investigation of the massless, two-dimentional, interacting field theories. Their basic property is their invariance under an infinite-dimensional group of conformal (analytic)
Vertex operators in the fractional quantum Hall effect
A second quantized formalism for electrons confined to a plane in a strong perpendicular magnetic field is constructed using vertex operators. They are seen to arise naturally from a holomorphic
Large scale physics of the quantum Hall fluid
Abstract We discuss the large-scale physics of incompressible Hall fluids from the point of view of universality and symmetry. We show that, in the scaling limit, incompressible Hall fluids are
Universality in quantum Hall systems
Abstract It is shown that the theory of the quantum Hall effect is closely related to Chern-Simons gauge theory and to rational conformal field theory. In particular, the equations of classical
Nonabelions in the fractional quantum Hall effect
Applications of conformal field theory to the theory of fractional quantum Hall systems are discussed. In particular, Laughlin's wave function and its cousins are interpreted as conformal blocks in
Duality in the quantum Hall system.
  • Lütken, Ross
  • Physics, Medicine
    Physical review. B, Condensed matter
  • 1992
We suggest that a unified description of the integer and fractional phases of the quantum Hall system may be possible if the scaling diagram of transport coefficients is invariant under linear
Paired Hall states
The principle that perturbation in quantum statistics should be accompanied by application of an appropriate magnetic field has been successful in giving a simple understanding of major qualitative
Elementary Theory: the Incompressible Quantum Fluid
In this lecture, I shall outline what I believe to be the correct fundamental picture of the fractional quantum Hall effect. The principal features of this picture are that the 1/3 state and its
...
1
2
3
4
5
...