# Conformal Field Theory of Composite Fermions

## Abstract

We show that the quantum Hall wave functions for the ground states in the Jain series {nu}=n/(2np+1) can be exactly expressed in terms of correlation functions of local vertex operators V{sub n} corresponding to composite fermions in the nth 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. Moreover, our construction shows how the states in the {nu}=n/(2np+1) Jain sequence may be interpreted as condensates of quasiparticles.

- Authors:

- Department of Physics, Stockholm University AlbaNova University Center, SE-106 91 Stockholm (Sweden)
- Physics Department, 104 Davey Lab, Pennsylvania State University, University Park, Pennsylvania 16802 (United States)
- Department of Physics, University of Oslo, P.O. Box 1048 Blindern, 0316 Oslo (Norway)

- Publication Date:

- OSTI Identifier:
- 20955475

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review Letters; Journal Volume: 98; Journal Issue: 7; Other Information: DOI: 10.1103/PhysRevLett.98.076801; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CONFORMAL INVARIANCE; CORRELATION FUNCTIONS; FERMIONS; GROUND STATES; QUANTUM FIELD THEORY; QUASI PARTICLES; TOPOLOGY; WAVE FUNCTIONS

### Citation Formats

```
Hansson, T. H., Chang, C.-C., Jain, J. K., and Viefers, S..
```*Conformal Field Theory of Composite Fermions*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVLETT.98.076801.

```
Hansson, T. H., Chang, C.-C., Jain, J. K., & Viefers, S..
```*Conformal Field Theory of Composite Fermions*. United States. doi:10.1103/PHYSREVLETT.98.076801.

```
Hansson, T. H., Chang, C.-C., Jain, J. K., and Viefers, S.. Fri .
"Conformal Field Theory of Composite Fermions". United States.
doi:10.1103/PHYSREVLETT.98.076801.
```

```
@article{osti_20955475,
```

title = {Conformal Field Theory of Composite Fermions},

author = {Hansson, T. H. and Chang, C.-C. and Jain, J. K. and Viefers, S.},

abstractNote = {We show that the quantum Hall wave functions for the ground states in the Jain series {nu}=n/(2np+1) can be exactly expressed in terms of correlation functions of local vertex operators V{sub n} corresponding to composite fermions in the nth 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. Moreover, our construction shows how the states in the {nu}=n/(2np+1) Jain sequence may be interpreted as condensates of quasiparticles.},

doi = {10.1103/PHYSREVLETT.98.076801},

journal = {Physical Review Letters},

number = 7,

volume = 98,

place = {United States},

year = {Fri Feb 16 00:00:00 EST 2007},

month = {Fri Feb 16 00:00:00 EST 2007}

}