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    Particle-Vortex Duality and the Modular Group: Applications to the Quantum Hall Effect and Other 2-D Systems


    Burgess, C. P. and Dolan, Brian P. (2001) Particle-Vortex Duality and the Modular Group: Applications to the Quantum Hall Effect and Other 2-D Systems. Physical Review B, 63 (15). pp. 155309-155330. ISSN 1098-0121

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    Abstract

    We show how particle-vortex duality implies the existence of a large non-abelian discrete symmetry group which relates the electromagnetic response for dual two-dimensional systems in a magnetic field. For conductors with charge carriers satisfying Fermi statistics (or those related to fermions by the action of the group), the resulting group is known to imply many, if not all, of the remarkable features of Quantum Hall systems. For conductors with boson charge carriers (modulo group transformations) a different group is predicted, implying equally striking implications for the conductivities of these systems, including a super-universality of the critical exponents for conductor/insulator and superconductor/insulator transitions in two dimensions and a hierarchical structure, analogous to that of the quantum Hall effect but different in its details. Our derivation shows how this symmetry emerges at low energies, depending only weakly on the details of dynamics of the underlying systems.

    Item Type: Article
    Additional Information: Preprint version of original article published by the American Physical Society DOI: 10.1103/PhysRevB.63.155309. We thank M. Hilke, C.A. Lutken, M. Paranjape, F. Quevedo and S. Sondhi for helpful discussions. C.B. is grateful to the University of Barcelona, D.A.M.T.P at Cambridge University, and the Aspen Centre for Physics, and B.D. to the Groupe de Physique Theorique, IPN, Orsay, and Dept. de Fisica, CINVESTAV, Mexico City, Mexico for their kind hospitality while part of this work was carried out. Our research has been assisted by financial support from N.S.E.R.C. (Canada), F.C.A.R. (Quebec), the Ambrose Monell Foundation, CNRS (France) and Enterprise Ireland, Basic Research Grant no. SC/1998/739.
    Keywords: Particle-Vortex; Duality; Modular Group; Quantum Hall Effect; 2-D Systems;
    Academic Unit: Faculty of Science and Engineering > Mathematical Physics
    Item ID: 2835
    Identification Number: https://doi.org/10.1103/PhysRevB.63.155309
    Depositing User: Dr. Brian Dolan
    Date Deposited: 16 Nov 2011 16:41
    Journal or Publication Title: Physical Review B
    Publisher: American Physical Society
    Refereed: No
    Funders: N.S.E.R.C. (Canada), Ambrose Monell Foundation, CNRS (France), Enterprise Ireland
    URI:

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