Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2003-04-11
Phys. Rev. B 68 (2003) 035327
Physics
Condensed Matter
Strongly Correlated Electrons
12 pages, no figures; a logical error below the proposed density operator (46) in version 1 is corrected, and the claim that t
Scientific paper
10.1103/PhysRevB.68.035327
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.
Hansson T. H.
Kailasvuori Janik
Karlhede Anders
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