Generalized Laughlin wave functions including the effect of Coulomb interaction.

We present improved wave functions for the ground state, Laughlin quasihole and quasiparticle excitations of the fractional quantum Hall effect. These depend explicitly on the effective strength of Coulomb interaction and reproduce Laughlin’s original result in the limit of no Coulomb interaction. PACS numbers: 73.40.Hm, 72.20.My Typeset using REVTEX 1 The fractional quantum Hall effect (FQHE) has attracted much interest since it was discovered in the 2D system of electrons subject to a high perpendicular magnetic field [1]. Laughlin first proposed a liquid-type ground state wave function (GSWF) [2]. His wave functions for the ground state, quasihole and quasiparticle excitations are independent of the effective strength of the inter-electron Coulomb interaction. However it has been observed in experiments that the energy gap is greatly reduced as the effective strength of Coulomb interaction increases [3]. After Laughlin’s seminal work, most of the discussions on the fractional quantum Hall effect using a microscopic trial wave function has been confined to the strong magnetic field limit, at which the effect of Landau level mixing can be ignored. The only exception is the recent work by Price et. al. [4] on the spherical geometry. Their trial wave function includes a term which is similar to the pseudopotential proposed by Ceperley [5] to include the effect of Coulomb interaction on the Wigner crystalization of the fermion one-component plasma. We present in this Letter a ground state wave function depending explictly on the Coulomb interaction, which is derived in a plausible manner from a Chern-Simons gauge field theory in the plane geometry. The modifying term is different from the term in Ref. [5]. Once a ground state wave function is given and if it is nondegenerate, wave functions for Laughlin quasihole and quasiparticle excitations can be written down directly following the Laughlin’s argument of adiabatic flux insertion. To support our reasoning, we also have done numerical calculations. We have compared numerically the Laughlin ground state wave function and our trial wave function in the case of up to five particles. This calculation shows the superiority of our trial wave function. This positive result provides a motivation for further numerical efforts. Let’s start with a non-relativistic Chern-Simons gauge field theory. The Hamiltonian is