Chern-Simons versus dipolar composite fermions at finite wavevector

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It was recently shown that dipolar composite fermions emerged from the lowest-Landau-level formulation of the quantum Hall effect give rise to similar results as those of the Chern-Simons gauge theory in the long wavelength and low energy limit. We ask whether this correspondence is still valid at finite wavevectors where the excitations do not necessarily look like dipolar quasiparticles. In particular, q=2kF density-density response function of the compressible state at ν=1/2 is evaluated in the low energy limit within the framework of the lowest-Landau-level theory. The imaginary parts of the density-density response functions at q=2kF of two theories have the same √ω dependence. However, the coefficient of the √ω term in the case of the lowest-Landau-level theory is not universal and can be much smaller than the corresponding coefficient in the Chern-Simons theory. We also discuss possible connection between these results and the recent experiment on phonon-mediated drag in the double-layer ν=1/2 system.