The Haldane-Rezayi quantum Hall state and conformal field theory

Research output: Contribution to journalArticleResearchpeer review

Authors

  • V. Gurarie
  • M. Flohr
  • C. Nayak

External Research Organisations

  • Institute for Advanced Studies
  • University of California at Santa Barbara
View graph of relations

Details

Original languageEnglish
Pages (from-to)513-538
Number of pages26
JournalNuclear Physics B
Volume498
Issue number3
Publication statusPublished - 11 Aug 1997
Externally publishedYes

Abstract

We propose field theories for the bulk and edge of a quantum Hall state in the universality class of the Haldane-Rezayi wavefunction. The bulk theory is associated with the c = -2 conformal field theory. The topological properties of the state, such as the quasiparticle braiding statistics and ground state degeneracy on a torus, may be deduced from this conformal field theory. The 10-fold degeneracy on a torus is explained by the existence of a logarithmic operator in the c = -2 theory; this operator corresponds to a novel bulk excitation in the quantum Hall state. We argue that the edge theory is the c = 1 chiral Dirac fermion, which is related in a simple way to the c = -2 theory of the bulk. This theory is reformulated as a truncated version of a doublet of Dirac fermions in which the SU(2) symmetry - which corresponds to the spin-rotational symmetry of the quantum Hall system - is manifest and non-local. We make predictions for the current-voltage characteristics for transport through point contacts.

Keywords

    Conformal field theory, Fractional quantum Hall effect, Non-abelian statistics

ASJC Scopus subject areas

Cite this

The Haldane-Rezayi quantum Hall state and conformal field theory. / Gurarie, V.; Flohr, M.; Nayak, C.
In: Nuclear Physics B, Vol. 498, No. 3, 11.08.1997, p. 513-538.

Research output: Contribution to journalArticleResearchpeer review

Gurarie V, Flohr M, Nayak C. The Haldane-Rezayi quantum Hall state and conformal field theory. Nuclear Physics B. 1997 Aug 11;498(3):513-538. doi: 10.48550/arXiv.cond-mat/9701212, 10.1016/S0550-3213(97)00351-9
Gurarie, V. ; Flohr, M. ; Nayak, C. / The Haldane-Rezayi quantum Hall state and conformal field theory. In: Nuclear Physics B. 1997 ; Vol. 498, No. 3. pp. 513-538.
Download
@article{ebe1c4e66f1e42a48f56132c9a23a8fe,
title = "The Haldane-Rezayi quantum Hall state and conformal field theory",
abstract = "We propose field theories for the bulk and edge of a quantum Hall state in the universality class of the Haldane-Rezayi wavefunction. The bulk theory is associated with the c = -2 conformal field theory. The topological properties of the state, such as the quasiparticle braiding statistics and ground state degeneracy on a torus, may be deduced from this conformal field theory. The 10-fold degeneracy on a torus is explained by the existence of a logarithmic operator in the c = -2 theory; this operator corresponds to a novel bulk excitation in the quantum Hall state. We argue that the edge theory is the c = 1 chiral Dirac fermion, which is related in a simple way to the c = -2 theory of the bulk. This theory is reformulated as a truncated version of a doublet of Dirac fermions in which the SU(2) symmetry - which corresponds to the spin-rotational symmetry of the quantum Hall system - is manifest and non-local. We make predictions for the current-voltage characteristics for transport through point contacts.",
keywords = "Conformal field theory, Fractional quantum Hall effect, Non-abelian statistics",
author = "V. Gurarie and M. Flohr and C. Nayak",
note = "(~) 1997 Published by Elsevier Science B.V. All rights reserved. PH S0550-32 1 3 (97)0035 1-9",
year = "1997",
month = aug,
day = "11",
doi = "10.48550/arXiv.cond-mat/9701212",
language = "English",
volume = "498",
pages = "513--538",
journal = "Nuclear Physics B",
issn = "0550-3213",
publisher = "Elsevier",
number = "3",

}

Download

TY - JOUR

T1 - The Haldane-Rezayi quantum Hall state and conformal field theory

AU - Gurarie, V.

AU - Flohr, M.

AU - Nayak, C.

N1 - (~) 1997 Published by Elsevier Science B.V. All rights reserved. PH S0550-32 1 3 (97)0035 1-9

PY - 1997/8/11

Y1 - 1997/8/11

N2 - We propose field theories for the bulk and edge of a quantum Hall state in the universality class of the Haldane-Rezayi wavefunction. The bulk theory is associated with the c = -2 conformal field theory. The topological properties of the state, such as the quasiparticle braiding statistics and ground state degeneracy on a torus, may be deduced from this conformal field theory. The 10-fold degeneracy on a torus is explained by the existence of a logarithmic operator in the c = -2 theory; this operator corresponds to a novel bulk excitation in the quantum Hall state. We argue that the edge theory is the c = 1 chiral Dirac fermion, which is related in a simple way to the c = -2 theory of the bulk. This theory is reformulated as a truncated version of a doublet of Dirac fermions in which the SU(2) symmetry - which corresponds to the spin-rotational symmetry of the quantum Hall system - is manifest and non-local. We make predictions for the current-voltage characteristics for transport through point contacts.

AB - We propose field theories for the bulk and edge of a quantum Hall state in the universality class of the Haldane-Rezayi wavefunction. The bulk theory is associated with the c = -2 conformal field theory. The topological properties of the state, such as the quasiparticle braiding statistics and ground state degeneracy on a torus, may be deduced from this conformal field theory. The 10-fold degeneracy on a torus is explained by the existence of a logarithmic operator in the c = -2 theory; this operator corresponds to a novel bulk excitation in the quantum Hall state. We argue that the edge theory is the c = 1 chiral Dirac fermion, which is related in a simple way to the c = -2 theory of the bulk. This theory is reformulated as a truncated version of a doublet of Dirac fermions in which the SU(2) symmetry - which corresponds to the spin-rotational symmetry of the quantum Hall system - is manifest and non-local. We make predictions for the current-voltage characteristics for transport through point contacts.

KW - Conformal field theory

KW - Fractional quantum Hall effect

KW - Non-abelian statistics

UR - http://www.scopus.com/inward/record.url?scp=0031564927&partnerID=8YFLogxK

U2 - 10.48550/arXiv.cond-mat/9701212

DO - 10.48550/arXiv.cond-mat/9701212

M3 - Article

AN - SCOPUS:0031564927

VL - 498

SP - 513

EP - 538

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -