Interacting electrons in magnetic fields: Tracking potentials and Jastrow-product wavefunctions

Details Interacting electrons in magnetic fields: Tracking potentials and Jastrow-product wavefunctions Interacting electrons in magnetic fields: Tracking potentials and Jastrow-product wavefunctions

1998-10-24

arxiv.org/abs/cond-mat/9810328v1

Phys. Rev. B 58, 1405 (1998)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

10 pages, 1 eps figure

Scientific paper

10.1103/PhysRevB.58.1405

The Schrodinger equation for an interacting spinless electron gas in a nonuniform magnetic field admits an exact solution in Jastrow product form when the fluctuations in the magnetic field track the fluctuations in the scalar potential. For tracking realizations in a two-dimensional electron gas, the degeneracy of the lowest Landau level persists, and the ``tracking'' solutions span the ground state subspace. In the context of the fractional quantum Hall problem, the Laughlin wave function is shown to be a tracking solution. Tracking solutions for screened Coulomb interactions are also constructed. The resulting wavefunctions are proposed as variational wave functions with potentially lower energy in the case of non-negligible Landau level mixing than the Laughlin function.

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