Composite fermion wave functions as conformal field theory correlators

Abstract

It is known that a subset of fractional quantum Hall wave functions has been expressed as conformal field theory (CFT) correlators, notably the Laughlin wave function at filling factor $\nu =1/m$ ($m$ odd) and its quasiholes, and the Pfaffian wave function at $\nu =1/2$ and its quasiholes. We develop a general scheme for constructing composite-fermion (CF) wave functions from conformal field theory. Quasiparticles at $\nu =1/m$ are created by inserting anyonic vertex operators, $P_{\frac{1}{m}}(z)$, that replace a subset of the electron operators in the correlator. The one-quasiparticle wave function is identical to the corresponding CF wave function, and the two-quasiparticle wave function has correct fractional charge and statistics and is numerically almost identical to the corresponding CF wave function. We further show how to exactly represent the CF wavefunctions in the Jain series $\nu =s/(2sp+1)$ as the CFT correlators of a new type of fermionic vertex operators, $V_{p,n}(z)$, constructed from $n$ free compactified bosons; these operators provide the CFT representation of composite fermions carrying $2p$ flux quanta in the $n^{\mathrm{th}}$ CF Landau level. We also construct the corresponding quasiparticle- and quasihole operators and argue that they have the expected fractional charge and statistics. For filling fractions 2/5 and 3/7 we show that the chiral CFTs that describe the bulk wave functions are identical to those given by Wen's general classification of quantum Hall states in terms of $K$-matrices and $l$- and $t$-vectors, and we propose that to be generally true. Our results suggest a general procedure for constructing quasiparticle wave functions for other fractional Hall states, as well as for constructing ground states at filling fractions not contained in the principal Jain series.

26 pages, 3 figures

References in corpus (2)

• Conformal Field Theory of Composite Fermions
• Berry phases for composite fermions: effective magnetic field and fractional statistics

Cited by in corpus (49)

• Topological Entanglement and Clustering of Jain Hierarchy States
• Quantum Hall physics in rotating Bose-Einstein condensates
• State Counting for Excited Bands of the Fractional Quantum Hall Effect: Exclusion Rules for Bound Excitons
• 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
• Quasiparticles and excitons for the Pfaffian quantum Hall state
• 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
• Nature of Quasielectrons and the Continuum of Neutral Bulk Excitations in the Laughlin Quantum Hall Fluids
• Quasihole condensates in quantum Hall liquids
• Partition Functions of Non-Abelian Quantum Hall States
• The Jain-2/5 parent Hamiltonian: structure of zero modes, dominance patterns, and zero mode generators
• A general approach to quantum Hall hierarchies
• The quantum Hall hierarchy in spherical geometry
• S3 Quantum Hall Wavefunctions
• Search for exact local Hamiltonians for general fractional quantum Hall states
• Effective Edge State Dynamics in the Fractional Quantum Hall Effect
• Partition Functions and Stability Criteria of Topological Insulators
• Quasielectrons as inverse quasiholes in lattice fractional quantum Hall models
• Topological d-wave pairing structures in Jain states
• Matrix product state representation of quasielectron wave functions
• Laughlin states and their quasi-particle excitations on the torus
• 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
• Exotic resonant level models in non-Abelian quantum Hall states coupled to quantum dots
• Hierarchical Nature of the Quantum Hall Effects
• Microscopic study of the 2/5 fractional quantum Hall edge
• Adiabatic Construction of Hierarchical Quantum Hall States
• Model wavefunctions for interfaces between lattice Laughlin states
• Success and failure of the plasma analogy for Laughlin states on a torus
• Entanglement Action for the Real-Space Entanglement Spectra of Composite Fermion Wave Functions
• Conformal field theory approach to parton fractional quantum Hall trial wave functions
• Inner workings of fractional quantum Hall parent Hamiltonians: A matrix product state point of view
• Composite Fermion Wavefunctions Derived by Conformal Field Theory
• Continuum limit of lattice quasielectron wavefunctions
• Microscopic derivation of Ginzburg-Landau theories for hierarchical quantum Hall states
• Generalization of Laughlin's Theory for the Fractional Quantum Hall Effect
• Laughlin's quasielectron as a non-local composite fermion
• Construction of a series of new $\nu =2/5$ fractional quantum Hall wave functions by conformal field theory
• Non-Fermi Liquid Quantum Impurity Physics from non-Abelian Quantum Hall States
• Conformal field theory construction for nonabelian hierarchy wave functions
• Fusion mechanism for quasiparticles and topological quantum order in the lowest Landau level
• Two-fluid theory of composite bosons and fermions and the quantum Hall proximity effect
• Linking infinite bond-dimension matrix product states with frustration-free Hamiltonians
• Anyon Dispersion in Aharonov-Casher Bands and Implications for Twisted MoTe${}_2$