Coherent Nonlinear Quantum Model for Composite Fermions

TL;DR

This paper models composite fermions in the fractional quantum Hall effect as a nonlinear, coherent mean-field quantum process using a 2D Schroedinger-Poisson model, aligning with known wave functions and offering a physical basis.

Contribution

It introduces a nonlinear, coherent mean-field quantum model for composite fermions, connecting phenomenological flux attachment to first-principles physics.

Findings

Model agrees with exact two-electron wave functions at filling factor 1/3

Provides a physical justification for composite fermions based on first principles

Demonstrates the nonlinear, coherent nature of the quantum process

Abstract

Originally proposed by Read [1] and Jain [2], the so-called "composite-fermion" is a phenomenological attachment of two infinitely thin local flux quanta seen as nonlocal vortices to two-dimensional (2D) electrons embedded in a strong orthogonal magnetic field. In this letter, it is described as a highly-nonlinear and coherent mean-field quantum process of the soliton type by use of a 2D stationary Schroedinger-Poisson differential model with only two Coulomb-interacting electrons. At filling factor $\nu={1}{3}$ of the lowest Landau level, it agrees with both the exact two-electron antisymmetric Schroedinger wave function and Laughlin's Jastrow-type guess for the fractional quantum Hall effect, hence providing this later with a tentative physical justification based on first principles.