Interacting electrons in magnetic fields

Tracking potentials and Jastrow-product wave functions

G. Fáth, Stephen B. Haley

Research output: Article

4 Citations (Scopus)

Abstract

The Schrödinger 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 wave functions are proposed as variational wave functions with potentially lower energy in the case of non-negligible Landau level mixing than the Laughlin function.

Original languageEnglish
Pages (from-to)1405-1413
Number of pages9
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume58
Issue number3
Publication statusPublished - júl. 15 1998

Fingerprint

Wave functions
wave functions
Magnetic fields
Electrons
products
magnetic fields
electron gas
Electron gas
electrons
Two dimensional electron gas
Coulomb interactions
nonuniform magnetic fields
Ground state
scalars
ground state
interactions
energy

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

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T2 - Tracking potentials and Jastrow-product wave functions

AU - Fáth, G.

AU - Haley, Stephen B.

PY - 1998/7/15

Y1 - 1998/7/15

N2 - The Schrödinger 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 wave functions are proposed as variational wave functions with potentially lower energy in the case of non-negligible Landau level mixing than the Laughlin function.

AB - The Schrödinger 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 wave functions 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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