### 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 ν=1 m (m odd) and its quasiholes, and the Pfaffian wave function at ν=1 2 and its quasiholes. We develop a general scheme for constructing composite-fermion (CF) wave functions from conformal field theory. Quasiparticles at ν=1 m are created by inserting anyonic vertex operators, P1 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 wave functions in the Jain series ν=s (2sp+1) as the CFT correlators of a new type of fermionic vertex operators, Vp,n (z), constructed from n free compactified bosons; these operators provide the CFT representation of composite fermions carrying 2p flux quanta in the nth 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.

Original language | English (US) |
---|---|

Article number | 075347 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 76 |

Issue number | 7 |

DOIs | |

State | Published - Aug 29 2007 |

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### All Science Journal Classification (ASJC) codes

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*76*(7), [075347]. https://doi.org/10.1103/PhysRevB.76.075347

}

*Physical Review B - Condensed Matter and Materials Physics*, vol. 76, no. 7, 075347. https://doi.org/10.1103/PhysRevB.76.075347

**Composite-fermion wave functions as correlators in conformal field theory.** / Hansson, T. H.; Chang, C. C.; Jain, J. K.; Viefers, S.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Composite-fermion wave functions as correlators in conformal field theory

AU - Hansson, T. H.

AU - Chang, C. C.

AU - Jain, J. K.

AU - Viefers, S.

PY - 2007/8/29

Y1 - 2007/8/29

N2 - 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 ν=1 m (m odd) and its quasiholes, and the Pfaffian wave function at ν=1 2 and its quasiholes. We develop a general scheme for constructing composite-fermion (CF) wave functions from conformal field theory. Quasiparticles at ν=1 m are created by inserting anyonic vertex operators, P1 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 wave functions in the Jain series ν=s (2sp+1) as the CFT correlators of a new type of fermionic vertex operators, Vp,n (z), constructed from n free compactified bosons; these operators provide the CFT representation of composite fermions carrying 2p flux quanta in the nth 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.

AB - 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 ν=1 m (m odd) and its quasiholes, and the Pfaffian wave function at ν=1 2 and its quasiholes. We develop a general scheme for constructing composite-fermion (CF) wave functions from conformal field theory. Quasiparticles at ν=1 m are created by inserting anyonic vertex operators, P1 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 wave functions in the Jain series ν=s (2sp+1) as the CFT correlators of a new type of fermionic vertex operators, Vp,n (z), constructed from n free compactified bosons; these operators provide the CFT representation of composite fermions carrying 2p flux quanta in the nth 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.

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U2 - 10.1103/PhysRevB.76.075347

DO - 10.1103/PhysRevB.76.075347

M3 - Article

AN - SCOPUS:34548442134

VL - 76

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 1098-0121

IS - 7

M1 - 075347

ER -