Determination of many-electron basis functions for a Quantum Hall ground state using Schur polynomials

TL;DR

This paper introduces a combinatorial method using Schur polynomials to determine many-electron basis functions for quantum Hall states, ensuring angular momentum symmetry and exemplifying with the 5/2 state.

Contribution

It presents a novel approach to derive basis functions for quantum Hall ground states using partition combinatorics and Schur polynomials, ensuring symmetry properties.

Findings

Derived basis functions for the 5/2 quantum Hall state.

Method guarantees angular momentum representation.

Applicable to other incompressible quantum Hall states.

Abstract

A method for determining the ground state of a planar interacting many-electron system in a magnetic field perpendicular to the plane is described. The ground state wave-function is expressed as a linear combination of a set of basis functions. Given only the flux and the number of electrons describing an incompressible state, we use the combinatorics of partitioning the flux among the electrons to derive the basis wave-functions as linear combinations of Schur polynomials. The procedure ensures that the basis wave-functions form representations of the angular momentum algebra. We exemplify the method by deriving the basis functions for the 5/2 quantum Hall state with a few particles.