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Mean field description of the fractional quantum Hall effect near nu = 1/(2k+1)

Apr, 1995
16 pages
Published in:
  • Int.J.Mod.Phys.A 11 (1996) 329-342
e-Print:
DOI:
Report number:
  • UBCTP-95-05
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Abstract:
The nature of Mean Field Solutions to the Equations of Motion of the Chern--Simons Landau--Ginsberg (CSLG) description of the Fractional Quantum Hall Effect (FQHE) is studied. Beginning with the conventional description of this model at some chemical potential μ0\mu_0 and magnetic field BB corresponding to a ``special'' filling fraction ν=2πρ/eB=1/n\nu=2\pi\rho/eB=1/n (n=1,3,5⋅⋅⋅n=1,3,5\cdot \cdot\cdot) we show that a deviation of μ\mu in a finite range around μ0\mu_0 does not change the Mean Field solution and thus the mean density of particles in the model. This result holds not only for the lowest energy Mean Field solution but for the vortex excitations as well. The vortex configurations do not depend on μ\mu in a finite range about μ0\mu_0 in this model. However when μ−μ0<μcr −\mu-\mu_0 < \mu_{cr}~- (or μ−μ0>μcr +\mu-\mu_0>\mu_{cr}~+) the lowest energy Mean Field solution describes a condensate of vortices (or antivortices). We give numerical examples of vortex and antivortex configurations and discuss the range of μ\mu and ν\nu over which the system of vortices is dilute.
Note:
  • Revtex document; 12 pages and 4 postscript figures in a file
  • Hall effect: fractional
  • gauge field theory
  • Chern-Simons term
  • Landau-Ginzburg model
  • mean field approximation
  • potential: chemical
  • magnetic field: external field
  • vortex: energy
  • vortex: density
  • numerical calculations