Model for the Fractional Quantum Hall Effect problem

TL;DR

This paper introduces a one-dimensional model that mimics the fractional quantum Hall effect, providing explicit wavefunctions for various filling factors and offering insights into the spectrum and ground states of the system.

Contribution

It presents a simple 1D model that reproduces key features of the fractional quantum Hall effect, including explicit ground state wavefunctions for odd-denominator fillings.

Findings

Wavefunctions resemble those of 2D electrons in Landau levels

Explicit ground state wavefunctions for filling factors v= N/M and v= 1-1/(2m+1)

Model captures spectrum and wavefunction characteristics of FQHE

Abstract

A simple one-dimensional model is proposed, in which N spinless repulsively interacting fermions occupy M>N degenerate states. It is argued that the energy spectrum and the wavefunctions of this system strongly resemble the spectrum and wavefunctions of 2D electrons in the lowest Landau level (the problem of the Fractional Quantum Hall Effect). In particular, Laughlin-type wavefunctions describe ground states at filling factors v = N/M = 1(2m+1). Within this model the complimentary wavefunction for v = 1-1/(2m + 1) is found explicitly and extremely simple ground state wavefunctions for arbitrary odd-denominator filling factors are proposed.