Composite-fermion wave functions as correlators in conformal field theory

T. H. Hansson, C. C. Chang, J. K. Jain, S. Viefers

Research output: Contribution to journalArticle

37 Citations (Scopus)

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 languageEnglish (US)
Article number075347
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume76
Issue number7
DOIs
StatePublished - Aug 29 2007

Fingerprint

Fermions
Correlators
Wave functions
correlators
fermions
wave functions
composite materials
Composite materials
operators
Set theory
set theory
apexes
Statistics
statistics
Bosons
Ground state
Mathematical operators
bosons
Fluxes

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

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

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 76, No. 7, 075347, 29.08.2007.

Research output: Contribution to journalArticle

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AU - Chang, C. C.

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