Details
| Original language | English |
|---|---|
| Journal | Physical Review B - Condensed Matter and Materials Physics |
| Volume | 67 |
| Issue number | 23 |
| Publication status | Published - 18 Jun 2003 |
Abstract
We propose to describe bulk wave functions of fractional quantum Hall states in terms of correlators of nonunitary b/c-spin systems. These yield a promising conformal field-theory analogon of the composite fermion picture of Jain. Fractional statistics are described by twist fields which naturally appear in the b/c-spin systems. We provide a geometrical interpretation of our approach in which bulk wave functions are seen as holomorphic functions over a ramified covering of the complex plane, where the ramification precisely resembles the fractional statistics of the quasiparticle excitations in terms of branch points on the complex plane. To extend Jain’s main series, we use the concept of composite fermions pairing to spin singlets, which enjoys a natural description in terms of the particular c = −2 b/c-spin system as known from the Haldane-Rezayi state. In this way we derive conformal field-theory proposals for lowest Landau-level bulk wave functions for more general filling fractions. We obtain a natural classification of the experimentally confirmed filling fractions, which does not contain prominent unobserved fillings. Furthermore, our scheme fits together with classifications in terms of K matrices of effective multilayer theories leading to striking restrictions of these coupling matrices.
ASJC Scopus subject areas
- Materials Science(all)
- Electronic, Optical and Magnetic Materials
- Physics and Astronomy(all)
- Condensed Matter Physics
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In: Physical Review B - Condensed Matter and Materials Physics, Vol. 67, No. 23, 18.06.2003.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Conformal field theory approach to bulk wave functions in the fractional quantum hall effect
AU - Flohr, Michael
AU - Osterloh, Klaus
PY - 2003/6/18
Y1 - 2003/6/18
N2 - We propose to describe bulk wave functions of fractional quantum Hall states in terms of correlators of nonunitary b/c-spin systems. These yield a promising conformal field-theory analogon of the composite fermion picture of Jain. Fractional statistics are described by twist fields which naturally appear in the b/c-spin systems. We provide a geometrical interpretation of our approach in which bulk wave functions are seen as holomorphic functions over a ramified covering of the complex plane, where the ramification precisely resembles the fractional statistics of the quasiparticle excitations in terms of branch points on the complex plane. To extend Jain’s main series, we use the concept of composite fermions pairing to spin singlets, which enjoys a natural description in terms of the particular c = −2 b/c-spin system as known from the Haldane-Rezayi state. In this way we derive conformal field-theory proposals for lowest Landau-level bulk wave functions for more general filling fractions. We obtain a natural classification of the experimentally confirmed filling fractions, which does not contain prominent unobserved fillings. Furthermore, our scheme fits together with classifications in terms of K matrices of effective multilayer theories leading to striking restrictions of these coupling matrices.
AB - We propose to describe bulk wave functions of fractional quantum Hall states in terms of correlators of nonunitary b/c-spin systems. These yield a promising conformal field-theory analogon of the composite fermion picture of Jain. Fractional statistics are described by twist fields which naturally appear in the b/c-spin systems. We provide a geometrical interpretation of our approach in which bulk wave functions are seen as holomorphic functions over a ramified covering of the complex plane, where the ramification precisely resembles the fractional statistics of the quasiparticle excitations in terms of branch points on the complex plane. To extend Jain’s main series, we use the concept of composite fermions pairing to spin singlets, which enjoys a natural description in terms of the particular c = −2 b/c-spin system as known from the Haldane-Rezayi state. In this way we derive conformal field-theory proposals for lowest Landau-level bulk wave functions for more general filling fractions. We obtain a natural classification of the experimentally confirmed filling fractions, which does not contain prominent unobserved fillings. Furthermore, our scheme fits together with classifications in terms of K matrices of effective multilayer theories leading to striking restrictions of these coupling matrices.
UR - http://www.scopus.com/inward/record.url?scp=3042853886&partnerID=8YFLogxK
U2 - 10.48550/arXiv.cond-mat/0208429
DO - 10.48550/arXiv.cond-mat/0208429
M3 - Article
AN - SCOPUS:3042853886
VL - 67
JO - Physical Review B - Condensed Matter and Materials Physics
JF - Physical Review B - Condensed Matter and Materials Physics
SN - 1098-0121
IS - 23
ER -