Exact eigenfunctions of FQHE systems at fractional filling factors 1/q. I. Formal results

TL;DR

This paper derives exact eigenfunctions for fractional quantum Hall effect systems at filling factors 1/q, revealing integrability properties and providing explicit wavefunctions and energy formulas for finite and infinite samples.

Contribution

It introduces a new class of exact eigenfunctions for FQHE at 1/q, connecting composite fermion states with Hartree-Fock orbitals and offering explicit energy formulas.

Findings

Eigenstates are expressed as Slater determinants of special orbitals.

The solutions suggest integrability in FQHE systems.

Energy formulas are provided for finite and thermodynamic limits.

Abstract

Eigenstates of the FQHE hamiltonian problem after to be projected on the LLL are determined for filling factors 1/q, with q an odd number. The solutions are found for an infinite class of finite samples in which the Coulomb potential is periodically extended. Therefore, a thermodynamic limit solution is also identified. The results suggest the presence of integrability properties in FQHE systems. The many particle states are simple Slater determinants constructed with special single particle states. These orbitals are defined as powers of order q of "composite fermion" like wavefunctions associated to a reduced magnetic field B/q. At the same time, those "composite fermion" states were obtained by factorizing and canceling fixed position (quasi-momentum independent) zeros in previously derived exact Hartree-Fock orbitals. A formula for the energy per particle of the FQHE states is given for finite samples as well as for the thermodynamic limit state. As a side result, the same "composite fermions" like orbitals are employed to construct variational wavefunctions of the system, showing zeros of order q as two electrons approach each other, as Laughlin states do. The long range spatial correlation associated to the starting HF solutions may further reduce the energy of these states.