An anyon wavefunction for the fractional quantum Hall effect

An anyon wavefunction (characterized by the statistical factor n) projected onto the lowest Landau level is derived for the fractional quantum Hall effect states at filling factor ν = n/(2 pn +1) (p and n are integers). We study the properties of the anyon wavefunction by using detailed Monte Carlo simulations in disc geometry and show that the anyon ground-state energy is a lower bound to the composite fermion one. Our results suggest that the composite fermions can be viewed as a combination of anyons and a fluid of charge–neutral dipoles. The fractional quantized Hall effect (FQHE) is one of the most fascinating phenomena in condensed-matter physics [1]. The pioneering work by Laughlin [2] based on the famous trial wavefunction at the filling of ν = 1/(2 p +1) revealed that the FQHE arises from the formation of an incompressible quantum fluid that supports quasiparticles and quasiholes carrying fractional charge and statistics. Jain’s composite fermion (CF) approach [3] successfully clarified fundamental aspects of the FQHE, which evolved into the description of the FQHE in terms of electron–vortex composites. A CF is the bound state of an electron and an even number of vortices formed in a two-dimensional (2D) system of electrons subject to a strong perpendicular magnetic field. On the basis of the CF theory, the interacting electrons at the Landau level (LL) filling factor ν = n/(2 pn+1), n and p being integers, transform into weakly interacting CFs with an effective filling factor ν = n, corresponding to n-filled CF LLs. The connection between the FQHE and the integer quantum Hall effect (IQHE) has motivated the Chern–Simons (CS) field theoretical approach [4, 5] for the FQHE. Within this field theoretical approach, an even number of magnetic flux quanta (φ0 = hc/e stands for one flux quantum) are attached to the 2D electrons through the introduction of a CS gauge field. In a mean-field approximation where the statistical gauge fluxes are delocalized from the electrons and uniformly spread out in the 2D plane, the average CS gauge field partially cancels the external magnetic field. So far, the fermion CS approach has been very successful for describing the nature of the quantum Hall state at ν = 1/2 where the CS-flux-generated fictitious magnetic field exactly cancels the external magnetic field at the mean-field level. 0953-8984/05/192977+07$30.00 © 2005 IOP Publishing Ltd Printed in the UK 2977