Density functional theory of the fractional quantum Hall effect

Abstract

A conceptual difficulty in formulating the density functional theory of the fractional quantum Hall effect is that while in the standard approach the Kohn-Sham orbitals are either fully occupied or unoccupied, the physics of the fractional quantum Hall effect calls for fractionally occupied Kohn-Sham orbitals. This has necessitated averaging over an ensemble of Slater determinants to obtain meaningful results. We develop an alternative approach in which we express and minimize the grand canonical potential in terms of the composite fermion variables. This provides a natural resolution of the fractional-occupation problem because the fully occupied orbitals of composite fermions automatically correspond to fractionally occupied orbitals of electrons. We demonstrate the quantitative validity of our approach by evaluating the density profile of fractional Hall edge as a function of temperature and the distance from the delta dopant layer and showing that it reproduces edge reconstruction in the expected parameter region.

References in corpus (23)

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• Imaging fractional incompressible stripes in integer quantum Hall systems
• Testing the topological nature of the fractional quantum Hall edge
• Hole-flux Composite Fermion Commensurability Oscillations
• Spin Ensemble Density Functional Theory for Inhomogeneous Quantum Hall Systems
• Composite Fermions with a Warped Fermi Contour
• Theoretical investigation of edge reconstruction in the $\nu$=5/2 and 7/3 fractional quantum Hall states
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• Density Functional Theory of Composite Fermions
• Edge reconstruction of fractional quantum Hall liquids with spin degrees of freedom

Cited by in corpus (13)

• Thirty Years of Composite Fermions and Beyond
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Kohn-Sham Theory of the Fractional Quantum Hall Effect
• Kohn-Sham Density Functional Theory of Abelian Anyons
• Crystalline Solutions of Kohn-Sham Equations in the Fractional Quantum Hall Regime
• Asymmetry of the Geometrical Resonances of Composite Fermions
• Mapping topology to nuclear dilaton-HLS effective field theory for dense baryonic matter
• Exact-exchange density functional theory of the integer quantum Hall effect: strict 2D limit
• Exact Exchange: a pathway for a Density Functional Theory of the Integer Quantum Hall Effect
• Fractionalized Kohn-Sham Scheme for Strongly Correlated Electrons
• Topological Phase Transitions of Interacting Fermions in the Presence of a Commensurate Magnetic Flux
• Mapping topology of skyrmions and fractional quantum Hall droplets to nuclear EFT for ultra-dense baryonic matter
• Developments in the applications of density functional theory to fractional quantum Hall systems