Jastrow form of the Ground State Wave Functions for Fractional Quantum Hall States

TL;DR

This paper introduces a novel method to determine the morphology of fractional quantum Hall ground states and constructs nearly exact wave functions based on flux-attachment, applicable across different interactions.

Contribution

It presents a new approach to derive ground state wave functions for fractional quantum Hall states using flux-attachment morphology in spherical geometry.

Findings

Constructed almost exact ground state wave functions for Coulomb interaction.

Morphology-based wave functions are robust across different electron interactions.

Provided a general method for determining quantum Hall state morphologies.

Abstract

The topological morphology--order of zeros at the positions of electrons with respect to a specific electron--of Laughlin state at filling fractions $1/m$ ($m$ odd) is homogeneous as every electron feels zeros of order $m$ at the positions of other electrons. Although fairly accurate ground state wave functions for most of the other quantum Hall states in the lowest Landau level are quite well-known, it had been an open problem in expressing the ground state wave functions in terms of flux-attachment to particles, {\em a la}, this morphology of Laughlin state. With a very general consideration of flux-particle relations only, in spherical geometry, we here report a novel method for determining morphologies of these states. Based on these, we construct almost exact ground state wave-functions for the Coulomb interaction. Although the form of interaction may change the ground state wave-function, the same morphology constructs the latter irrespective of the nature of the interaction between electrons.