On the Structure of Edge State Inner Products in the Fractional Quantum Hall Effect

Abstract

We analyse the inner products of edge state wavefunctions in the fractional quantum Hall effect, specifically for the Laughlin and Moore-Read states. We use an effective description for these inner products given by a large-$N$ expansion ansatz proposed in recent work by J. Dubail, N. Read and E. Rezayi, PRB 86, 245310 (2012). As noted by these authors, the terms in this ansatz can be constrained using symmetry, a procedure we perform to high orders. We then check this conjecture by calculating the overlaps exactly for small system sizes and compare the numerics with our high-order expansion. We find the effective description to be very accurate.

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• Thirty Years of Composite Fermions and Beyond
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Effective Edge State Dynamics in the Fractional Quantum Hall Effect
• Entanglement Action for the Real-Space Entanglement Spectra of Composite Fermion Wave Functions
• Destructive quantum interference in transport through molecules with electron-electron and electron-vibration interactions
• Conformal field theory approach to parton fractional quantum Hall trial wave functions
• Almost linear Haldane pseudopotentials and emergent conformal block wave-functions in a Landau level