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Noncommutative Field Theory and the Dynamics of Quantum Hall Fluids

J. L. F. Barbon·A. Paredes
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Abstract

We study the spectrum of density fluctuations of Fractional Hall Fluids in the context of the noncommutative hidrodynamical model of Susskind. We show that, within the weak-field expansion, the leading correction to the noncommutative Chern--Simons Lagrangian (a Maxwell term in the effective action,) destroys the incompressibility of the Hall fluid due to strong UV/IR effects at one loop. We speculate on possible relations of this instability with the transition to the Wigner crystal, and conclude that calculations within the weak-field expansion must be carried out with an explicit ultraviolet cutoff at the noncommutativity scale. We point out that the noncommutative dipoles exactly match the spatial structure of the Halperin--Kallin quasiexcitons. Therefore, we propose that the noncommutative formalism must describe accurately the spectrum at very large momenta, provided no weak-field approximations are made. We further conjecture that the noncommutative open Wilson lines are `vertex operators' for the quasiexcitons.

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J. L. F. Barbon, A. Paredes. 2001-12-19. Noncommutative Field Theory and the Dynamics of Quantum Hall Fluids. https://doi.org/10.1142/s0217751x02011011

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