Anyon Wave Function for the Fractional Quantum Hall Effect

TL;DR

This paper derives an anyon wave function for fractional quantum Hall states, demonstrating through Monte Carlo simulations that it provides a lower bound to the composite fermion ground-state energy.

Contribution

It introduces a new anyon wave function for fractional quantum Hall states and analyzes its properties using Monte Carlo simulations.

Findings

Anyon wave function is a lower bound to composite fermion energy.

Monte Carlo simulations validate the properties of the anyon wave function.

The wave function applies to filling factors ν = n/(2pn+1).

Abstract

An anyon wave function (characterized by the statistical factor $n$) projected onto the lowest Landau level is derived for the fractional quantum Hall effect states at filling factor $\nu = n/(2pn+1)$ ($p$ and $n$ are integers). We study the properties of the anyon wave function by using detailed Monte Carlo simulations in disk geometry and show that the anyon ground-state energy is a lower bound to the composite fermion one.