Composite fermions from the algebraic point of view

TL;DR

This paper presents an algebraic approach to composite fermions, showing how their wavefunctions can be derived using operator methods and explicitly solving the system for harmonic interactions, revealing a boson-fermion correspondence.

Contribution

It introduces an algebraic framework for composite fermion wavefunctions and provides an exact solution for harmonic interactions in the lowest Landau level.

Findings

Wavefunctions derived via normal ordered products of operators.

Exact solution for harmonic interactions in lowest Landau level.

Explicit demonstration of boson-fermion correspondence.

Abstract

Composite fermion wavefuctions have been used to describe electrons in a strong magnetic field. We show that the polynomial part of these wavefunctions can be obtained by applying a normal ordered product of suitably defined annihilation and creation operators to an even power of the Vandermonde determinant, which can been considered as a kind of a non-trivial Fermi sea. In the case of the harmonic interaction we solve the system exactly in the lowest Landau level. The solution makes explicit the boson-fermion correspondence proposed recently.