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.

arXiv comment1 color figure; new result on exact correspondence between CF wave functions and CFT correlators included; presentation made less technical; some references changed

References in corpus (6)

• $2n$ Quasihole States Realize $2^{n-1}$-Dimensional Spinor Braiding Statistics in Paired Quantum Hall States
• A Plasma Analogy and Berry Matrices for Non-Abelian Quantum Hall States
• Nature of quasiparticle excitations in the fractional quantum Hall effect
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Cited by in corpus (31)

• Quantum Hall system in Tao-Thouless limit
• Topological Entanglement and Clustering of Jain Hierarchy States
• Quantum Hall physics in rotating Bose-Einstein condensates
• Clustering Properties and Model Wavefunctions for Non-Abelian Fractional Quantum Hall Quasielectrons
• Composite fermion wave functions as conformal field theory correlators
• Microscopic theory of the quantum Hall hierarchy
• Quantum Hall quasielectron operators in conformal field theory
• Hall Viscosity of Hierarchical Quantum Hall States
• Quantum Hall quasielectrons - Abelian and non-Abelian
• 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
• Emergent particle-hole symmetry in spinful bosonic quantum Hall systems
• Quasihole condensates in quantum Hall liquids
• Quantum gravity as a Fermi liquid
• A general approach to quantum Hall hierarchies
• Composite Fermion states on the torus
• Search for exact local Hamiltonians for general fractional quantum Hall states
• Partition Functions and Stability Criteria of Topological Insulators
• Matrix product state representation of quasielectron wave functions
• The Gaffnian and Haffnian: physical relevance of non-unitary CFT for incompressible fractional quantum Hall effect
• Composite fermion model for entanglement spectrum of fractional quantum Hall states
• Hierarchical Nature of the Quantum Hall Effects
• Success and failure of the plasma analogy for Laughlin states on a torus
• Composite Fermion Wavefunctions Derived by Conformal Field Theory
• Microscopic derivation of Ginzburg-Landau theories for hierarchical quantum Hall states
• Construction of a series of new $\nu =2/5$ fractional quantum Hall wave functions by conformal field theory
• Conformal field theory construction for nonabelian hierarchy wave functions
• Quantum impurity models from conformal field theory
• Fractional quantum Hall edge polaritons