Exact Analytic Results for Composite Fermions in a Rajaraman-Sondhi like formulation

TL;DR

This paper derives exact energy spectra and ground states for two composite fermions in a magnetic field, providing insights into their behavior and supporting the validity of Laughlin and Jain wave-functions.

Contribution

It presents the first exact analytic solutions for composite fermions in a specific formulation, elucidating their energetic properties and stability.

Findings

Energy eigenvalues decrease with angular momentum

Composite fermions tend to stay apart energetically

Supports Laughlin and Jain wave-function validity

Abstract

We obtain the exact spectrum and the unique ground state of two composite fermions (in a Rajaraman - Sondhi like formulation) in an external magnetic field $B$. We show that the energy eigenvalues decrease with increasing angular momentum, thus making it energetically favourable for composite fermions to stay apart. Generalising this result to a gas of composite fermions, we provide an energetic justification of the Laughlin and Jain wave-functions.