Burgess, C. P. and Dolan, Brian P.
Particle-Vortex Duality and the Modular Group:
Applications to the Quantum Hall Effect and Other 2-D Systems.
Physical Review B, 63 (15).
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
||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.
||Particle-Vortex; Duality; Modular Group; Quantum Hall Effect; 2-D Systems;
||Science & Engineering > Mathematical Physics
Dr. Brian Dolan
||16 Nov 2011 16:41
|Journal or Publication Title:
||Physical Review B
||American Physical Society
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