Charge and Current in the Quantum Hall Matrix Model

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 obtai...

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Bibliographic Details
Published in:arXiv.org 2004-06
Main Authors: Hansson, T H, Kailasvuori, J, Karlhede, A
Format: Article
Language:English
Subjects:
Commutators
Conductivity
Couplings
Density
Magnetic fields
Mathematical analysis
Matrix methods
Operators (mathematics)
Quantum theory
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.0304271