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

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.

10 pages

References in corpus (8)

• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• $2n$ Quasihole States Realize $2^{n-1}$-Dimensional Spinor Braiding Statistics in Paired Quantum Hall States
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Fractional Quantum Hall States and Jack Polynomials
• Possible Pairing-Induced Even-Denominator Fractional Quantum Hall Effect in the Lowest Landau Level
• Analytic calculations of trial wave functions of the fractional quantum Hall effect on the sphere

Cited by in corpus (2)

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