Ground States of Quantum Hall Three-Body ``Short-Range'' Repulsion and Mean Field Approximation: Correlation Functions and Overlaps

Abstract

We analyze properties of trial wave functions in fractional quantum Hall effect, generated by the "short-range", three-body repulsion and its mean field approximation. Ground states of electron repulsion Hamiltonians at filing factor ν = 1/2 are evaluated as a description of physically observed state ν = 5/2. We analyze overlaps between the Moore-Read state and its mean field approximation for different number of particles and compare both states with ground state of the Coulomb interaction in the first excited Landau level. Our study also includes examination of electron-electron correlation functions and electron densities of excited states for both interactions.