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 semiclassical regime for these states, thereby relating their stability to their semiclassical nature. The equivalent problem of two-dimensional plasmas is solved analytically, to leading order for $N\to \infty$, by the saddle point approximation - a two-dimensional extension of the method used in random matrix models of quantum gravity and gauge theories. To leading order, the Laughlin states describe classical droplets of fluids with uniform density and sharp boundaries, as expected from the Laughlin ``plasma analogy''. In this limit, the dynamical $W_{\infty }$-symmetry of the quantum Hall states expresses the kinematics of the area-preserving deformations of incompressible liquid droplets.

13 pages (+1 figure, available upon request), CERN-TH 6810/93

References in corpus (6)

• Infinite Symmetry in the Quantum Hall Effect
• Fermions in the Lowest Landau Level: Bosonization, $W_{\infty }$ Algebra, Droplets, Chiral Boson
• Conformal Symmetry and Universal Properties of Quantum Hall States
• One-Dimensional Fermions as Two-Dimensional Droplets Via Chern-Simons Theory
• W-Infinity and String Theory
• Charge distribution in two-dimensional electrostatics

Cited by in corpus (38)

• Thermal Transport in Chiral Conformal Theories and Hierarchical Quantum Hall States
• Lowest-Landau-level theory of the quantum Hall effect: the Fermi-liquid-like state
• Edge state inner products and real-space entanglement spectrum of trial quantum Hall states
• Modular Invariant Partition Functions in the Quantum Hall Effect
• Stable Hierarchical Quantum Hall Fluids as W-(1 + infinity) Minimal Models
• Noncommutative geometry for three-dimensional topological insulators
• Classification of Quantum Hall Universality Classes by $W_{1+\infty }$ symmetry
• Noncommutative Superspace, Supermatrix and Lowest Landau Level
• Volume-preserving diffeomorphism as nonabelian higher-rank gauge symmetry
• W_{\infty} Gauge Transformations and the Electromagnetic Interactions of Electrons in the Lowest Landau Level
• Slater Decomposition of Laughlin States
• Quantum Hall phases and plasma analogy in rotating trapped Bose gases
• Algebraic Aspects of the Fractional Quantum Hall Effect
• Infinite Symmetry in the Fractional Quantum Hall Effect
• $W_{\infty }$ Algebras in the Quantum Hall Effect
• Multipole Expansion in the Quantum Hall Effect
• Theory of fractional quantum Hall interferometers
• Hamiltonian Formulation of the W-Infinity Minimal Models
• Matrix Model Description of Laughlin Hall States
• Numerical Study of Hierarchical Hall Edge States on the Disk Geometry
• N=1 Locally Supersymmetric Standard Models from Intersecting Branes
• Jain States in a Matrix Theory of the Quantum Hall Effect
• W-infinity Symmetry in the Quantum Hall Effect Beyond the Edge
• 2D Superconductivity: Classification of Universality Classes by Infinite Symmetry
• Bulk-Boundary Correspondence in the Quantum Hall Effect
• The Quantum Hall Effect with Wilczek's charged magnetic flux tubes instead of electrons
• Higher algebras and mesonic spectrum in two-dimensional QCD
• Electrons in a Strong Magnetic Field on a Disk
• Edge excitations of the Chern Simons matrix theory for the FQHE
• Dynamics of Quantum Hall Interfaces
• Conformal field theory approach to parton fractional quantum Hall trial wave functions
• Spontaneous Symmetry Breaking in the Non-Abelian Anyon Fluid
• Hom-Lie-Virasoro symmetries in Bloch electron systems and quantum plane in tight binding models
• Matrix Effective Theories of the Fractional Quantum Hall effect
• Synthetic anyons in noninteracting systems
• Moyal product and Generalized Hom-Lie-Virasoro symmetries in Bloch electron systems
• Semiclassical Droplet States in Matrix Quantum Hall Effect
• Noncommutative Solitons and the W_{1+\infty} Algebras in Quantum Hall Theory