Charge and Current in the Quantum Hall Matrix Model

Abstract

We extend the quantum Hall matrix model to include couplings to external electric and magnetic fields. The associated current suffers from matrix ordering ambiguities even at the classical level. We calculate the linear response at low momenta -- this is unambigously defined. In particular, we obtain the correct fractional quantum Hall conductivity, and the expected density modulations in response to a weak and slowly varying magnetic field. These results show that the classical quantum Hall matrix models describe important aspects of the dynamics of electrons in the lowest Landau level. In the quantum theory the ordering ambiguities are more severe; we discuss possible strategies, but we have not been able to construct a good density operator, satisfying the pertinent lowest Landau level commutator algebra.

12 pages, no figures; a logical error below the proposed density operator (46) in version 1 is corrected, and the claim that this density operator satisfy the magnetic algebra (2) is withdrawn. Some formulations have been changed and a few misprints corrected

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• On Level Quantization for the Noncommutative Chern-Simons Theory
• Quantum Hall Physics = Noncommutative Field Theory
• Quantum Hall states on the cylinder as unitary matrix Chern-Simons theory
• Chern-Simons matrix model: coherent states and relation to Laughlin wavefunctions
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Cited by in corpus (15)

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• The Quantum Hall Effect in Supersymmetric Chern-Simons Theories
• Matrix Model Description of Laughlin Hall States
• Jain States in a Matrix Theory of the Quantum Hall Effect
• Geometric quench in the fractional quantum Hall effect: exact solution in quantum Hall matrix models and comparison with bimetric theory
• Fractional quantum Hall effect on the two-sphere: a matrix model proposal
• Hall viscosity and geometric response in the Chern-Simons matrix model of the Laughlin states
• Lowest Landau level theory of the bosonic Jain states
• Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields
• ADHM and the 4d Quantum Hall Effect
• Noncommutative Fluids
• Edge excitations of the Chern Simons matrix theory for the FQHE
• Solitons and Quasielectrons in the Quantum Hall Matrix Model
• Matrix Effective Theories of the Fractional Quantum Hall effect
• Semiclassical Droplet States in Matrix Quantum Hall Effect