Conformal Field Theory of Composite Fermions

Abstract

We show that the quantum Hall wave functions for the ground states in the Jain series can be exactly expressed in terms of correlation functions of local vertex operators, V_n, corresponding to composite fermions in the n:th composite-fermion (CF) Landau level. This allows for the powerful mathematics of conformal field theory to be applied to the successful CF phenomenology. Quasiparticle and quasihole states are expressed as correlators of anyonic operators with fractional (local) charge, allowing a simple algebraic understanding of their topological properties that are not manifest in the CF wave functions.

1 color figure; new result on exact correspondence between CF wave functions and CFT correlators included; presentation made less technical; some references changed

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• Quantum Hall wave functions on the torus
• Hierarchy wave functions--from conformal correlators to Tao-Thouless states
• Composite Fermions on a Torus
• Domain walls, fusion rules and conformal field theory in the quantum Hall regime
• Quantum gravity as a Fermi liquid
• Conformal field theory construction for nonabelian hierarchy wave functions
• Construction of a series of new $\nu =2/5$ fractional quantum Hall wave functions by conformal field theory
• Fractional quantum Hall edge polaritons