Quantum Hall Physics = Noncommutative Field Theory

Abstract

In this note, we study a matrix-regularized version of non-commutative U(1) Chern-Simons theory proposed recently by Polychronakos. We determine a complete minimal basis of exact wavefunctions for the theory at arbitrary level k and rank N and show that these are in one-to-one correspondence with Laughlin-type wavefunctions describing excitations of a quantum Hall droplet composed of N electrons at filling fraction 1/k. The finite matrix Chern-Simons theory is shown to be precisely equivalent to the theory of composite fermions in the lowest Landau level, believed to provide an accurate description of the filling fraction 1/k fractional quantum Hall state. In the large N limit, this implies that level k noncommutative U(1) Chern-Simons theory is equivalent to the Laughlin theory of the filling fraction 1/k quantum Hall fluid, as conjectured recently by Susskind.

17 pages, LaTeX, v2: references and comment added

Cited by in corpus (83)

• Physics and Mathematics of Calogero particles
• Duality in Scalar Field Theory on Noncommutative Phase Spaces
• Fractional Quantum Hall Effect via Holography: Chern-Simons, Edge States, and Hierarchy
• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• A translation-invariant renormalizable non-commutative scalar model
• Vacuum configurations for renormalizable non-commutative scalar models
• Interactions and non-commutativity in quantum Hall systems
• Higher-Dimensional Quantum Hall Effect in String Theory
• Quantum Gravity, Field Theory and Signatures of Noncommutative Spacetime
• On the vacuum states for noncommutative gauge theory
• Quantum mechanics on noncommutative Riemann surfaces
• Noncommutative field theories on $R_{\lambda }^3$: Towards UV/IR mixing freedom
• Geometric quench and nonequilibrium dynamics of fractional quantum Hall states
• Matrix Model for De Sitter
• Non-Abelian 3d Bosonization and Quantum Hall States
• Overview of the parametric representation of renormalizable non-commutative field theory
• Commutative limit of a renormalizable noncommutative model
• Noncommutative Quantum Mechanics and rotating frames
• Parametric representation of "critical" noncommutative QFT models
• The Quantum Hall Effect in Supersymmetric Chern-Simons Theories
• Deformed Two-Photon Squeezed States in Noncommutative Space
• NC Branes and Hierarchies in Quantum Hall Fluids
• A Matrix Model for Non-Abelian Quantum Hall States
• Open Dielectric Branes
• Coherent States of the Deformed Heisenberg-Weyl Algebra in Noncommutative Space
• Noncommutative Field Theory and the Dynamics of Quantum Hall Fluids
• Curing the UV/IR mixing for field theories with translation-invariant $\star$ products
• Matrix Model Description of Laughlin Hall States
• Quantum SU(2$|$1) supersymmetric Calogero-Moser spinning systems
• Charge and Current in the Quantum Hall Matrix Model
• D-string fluid in conifold: I. Topological gauge model
• Jain States in a Matrix Theory of the Quantum Hall Effect
• A Quantum Hall Fluid of Vortices
• D-string fluid in conifold: II. Matrix model for D-droplets on S^{3} and S^{2}
• Lattice Perturbation Theory in Noncommutative Geometry and Parity Anomaly in 3D Noncommutative QED
• Geometric quench in the fractional quantum Hall effect: exact solution in quantum Hall matrix models and comparison with bimetric theory
• Entanglement in the Quantum Hall Matrix Model
• Pauli Oscillator In Noncommutative Space
• Fermions on tori in uniform abelian fields
• Hall viscosity and geometric response in the Chern-Simons matrix model of the Laughlin states
• Fractional quantum Hall effect on the two-sphere: a matrix model proposal
• Noncommutative Field Theory of the Tkachenko Mode: Symmetries and Decay Rate
• Anisotropic Quantum Hall Droplets
• Quantum aspects of Seiberg-Witten map in noncommutative Chern-Simons theory
• Lowest Landau level theory of the bosonic Jain states
• Searching for Effects of Spatial Noncommutativity via Chern-Simons' Processes
• NC Effective Gauge Model for Multilayer FQH States
• Collective Field Formulation of the Multispecies Calogero Model and its Duality Symmetries
• Description of identical particles via gauged matrix models : a generalization of the Calogero-Sutherland system
• Hall Viscosity in the Non-Abelian Quantum Hall Matrix Model
• Tales of D0 on D6 Branes: Matrix Mechanics of Identical Particles
• Noncommutative Maxwell-Chern-Simons theory (I): One-loop dispersion relation analysis
• Dualities in Quantum Hall System and Noncommutative Chern-Simons Theory
• Supersymmetric non-Abelian noncommutative Chern-Simons theory
• The Quantum Hydrodynamics of the Sutherland Model
• ADHM and the 4d Quantum Hall Effect
• Noncommutative Fluids
• Edge excitations of the Chern Simons matrix theory for the FQHE
• Finite Chern-Simons matrix model - algebraic approach
• Algebra of the observables in the Calogero model and in the Chern-Simons matrix model
• A note on broken dilatation symmetry in planar noncommutative theory
• Matrix supergroup Chern-Simons models for vortex-antivortex systems
• Induced magnetic moment in noncommutative Chern-Simons scalar QED
• A Matrix Model for Fractional Quantum Hall States
• Vortex counting and the quantum Hall effect
• On the quantum equivalence of commutative and noncommutative Chern-Simons theories at higher orders
• A Matrix Model for Bilayered Quantum Hall Systems
• Spectral theorem in noncommutative field theories: Jacobi dynamics
• Noncommutative gauge symmetry in the fractional quantum Hall effect
• Matrix Effective Theories of the Fractional Quantum Hall effect
• Twisted Conformal Field Theories and Morita equivalence
• Semiclassical Droplet States in Matrix Quantum Hall Effect
• On plane wave and vortex-like solutions of noncommutative Maxwell-Chern-Simons theory
• Matrix oscillator and Laughlin Hall states
• Quasi-hole solutions in finite noncommutative Maxwell-Chern-Simons theory
• Paired quantum Hall states on noncommutative two-tori
• Non-commutative effective field theory of the lowest Landau level superfluid
• 5d-4d Correspondence in Twisted M-theory on a Conifold
• Fermion liquids as quantum Hall liquids in phase space: A unified approach for anomalies and responses
• Solitons in finite droplets of noncommutative Maxwell-Chern-Simons theory
• Lattice oscillator model on noncommutative space: eigenvalues problem for the perturbation theory
• Quantum Algebra of Chern-Simons Matrix Model and Large $N$ Limit
• A symplectic geometric origin of universal quartic modified dispersion relations