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

TL;DR

This paper finds exact solutions for interacting electrons in nonuniform magnetic fields using Jastrow wavefunctions, revealing new variational states that may improve energy estimates in quantum Hall systems.

Contribution

It introduces the concept of tracking solutions where magnetic and scalar potential fluctuations align, providing exact wavefunctions and extending the Laughlin state framework.

Findings

Tracking solutions preserve Landau level degeneracy.

The Laughlin wave function is a special tracking solution.

Constructed variational wavefunctions may lower energy estimates.

Abstract

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.