# New exact analytical results for two quasiparticle excitation in the fractional quantum Hall effect

## TL;DR

This paper analytically calculates two quasiparticle excitation energies in fractional quantum Hall systems, comparing Laughlin and composite fermion theories, and finds that CF wavefunctions generally have lower energies, with differences diminishing as system size grows.

## Contribution

It provides the first exact analytical results for two quasiparticle energies in small fractional quantum Hall systems considering full Coulomb interactions.

## Key findings

- CF wavefunctions have lower energy than Laughlin wavefunctions.
- Energy difference decreases with increasing system size.
- Results confirm the stability of composite fermion states.

## Abstract

In this work, two quasiparticle excitation energies per particle are calculated analytically for systems with up to $N = 7$ electrons in both Laughlin and composite fermions (CF) theories by considering the full jellium potential which consists of three parts, the electron-electron, electron-background, and background-background Coulomb interactions. The exact results we have obtained confirm the fact that the CF-wavefunction for two quasiparticles has lower energy than Laughlin wavefunction though the found difference between Laughlin and (CF) two quasiparticle energies decreases as the system size increases.