The Fermion-Boson Transformation in Fractional Quantum Hall Systems

Abstract

A Fermion to Boson transformation is accomplished by attaching to each Fermion a single flux quantum oriented opposite to the applied magnetic field. When the mean field approximation is made in the Haldane spherical geometry, the Fermion angular momentum $l_F$ is replaced by $l_B=l_F-\frac{1}{2}(N-1)$. The set of allowed total angular momentum multiplets is identical in the two different pictures. The Fermion and Boson energy spectra in the presence of many body interactions are identical if and only if the pseudopotential is ``harmonic'' in form. However, similar low energy bands of states with Laughlin correlations occur in the two spectra if the interaction has short range. The transformation is used to clarify the relation between Boson and Fermion descriptions of the hierarchy of condensed fractional quantum Hall states.

arXiv comment5 pages, 4 figures, submitted to Physica E

References in corpus (6)

• Quasiparticle Interactions in Fractional Quantum Hall Systems: Justification of Different Hierarchy Schemes
• The Composite Fermion Hierarchy: Condensed States of Composite Fermion Excitations?
• Composite Fermions and quantum Hall systems: Role of the Coulomb pseudopotential
• Composite Fermions and the Fractional Quantum Hall Effect: Essential Role of the Pseudopotential
• Hund's Rule for Monopole Harmonics, or Why the Composite Fermion Picture Works
• Composite Fermions in Fractional Quantum Hall Systems

Cited by in corpus (5)

• Composite fermion theory of rapidly rotating two-dimensional bosons
• The Hierarchy of Incompressible Fractional Quantum Hall States
• Novel Families of Fractional Quantum Hall States: Pairing of Composite Fermions
• Fractional quantum Hall effect and electron correlations in partially filled first excited Landau level
• Interaction and Particle-Hole Symmetry of Laughlin Quasiparticles