Particle-Hole Duality in the Lowest Landau Level

Abstract

We derive a number of exact relations between response functions of holomorphic, chiral fractional quantum Hall states and their particle-hole (PH) conjugates. These exact relations allow one to calculate the Hall conductivity, Hall viscosity, various Berry phases, and the static structure factor of PH-conjugate states from the corresponding properties of the original states. These relations establish a precise duality between chiral quantum Hall states and their PH-conjugates. The key ingredient in the proof of the relations is a generalization of Girvin's construction of PH-conjugate states to inhomogeneous magnetic field and curvature. Finally, we make several non-trivial checks of the relations, including for the Jain states and their PH-conjugates.

10 pages

References in corpus (9)

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Cited by in corpus (24)

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• Bimetric Theory of Fractional Quantum Hall States
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• Fermi wave vector for the non-fully spin polarized composite-fermion Fermi sea
• Quench dynamics of collective modes in fractional quantum Hall bilayers
• Multiple Magnetorotons and Spectral Sum Rules in Fractional Quantum Hall Systems
• Fractional quantum Hall systems near nematicity: bimetric theory, composite fermions, and Dirac brackets
• Dirac Fermion Hierarchy of Composite Fermi Liquids
• $s$-wave paired composite-fermion electron-hole trial state for quantum Hall bilayers with $\nu =1$
• Dirac Composite Fermion Theory of General Jain's Sequences
• Collective excitations at filling factor 5/2: The view from superspace
• Particle-hole symmetry for composite fermions: An emergent symmetry in the fractional quantum Hall effect
• Berry phase of the composite-fermion Fermi Sea: Effect of Landau-level mixing
• Geometric responses of the Pfaffian state
• Algebraic Approach to Fractional Quantum Hall Effect
• Static structure factor and the dispersion of the Girvin-MacDonald-Platzman density mode for fractional quantum Hall fluids on the Haldane sphere
• A numerical study of bounds in the correlations of fractional quantum Hall states
• Very high-energy collective states of partons in fractional quantum Hall liquids
• Electrons and composite Dirac fermions in the lowest Landau level
• Scale Invariance in the Lowest Landau Level
• Chiral Metric Hydrodynamics, Kelvin Circulation Theorem, and the Fractional Quantum Hall Effect
• Dispersion of collective modes in spinful fractional quantum Hall states on the sphere
• Bosonic Holes in Quadratic Bosonic Systems