Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2010-06-30
Physics
Condensed Matter
Strongly Correlated Electrons
7 pages, 6 eps figures
Scientific paper
Dualities are deep conceptual tools in many areas of physics and mathematics; in particular, electric-magnetic (EM) duality has a long tradition ranging from Dirac's magnetic poles to S-duality in string and field theory. Here we investigate the duality structure in quantum lattice systems with topological order, a collective order also appearing in fractional quantum Hall systems. We define EM duality for all of Kitaev's quantum double models based on discrete gauge theories with Abelian and non-Abelian groups, and identify its natural habitat as a new class of topological models based on Hopf algebras. We interpret these as extended string-net models, whereupon Levin and Wen's string-nets, which describe all topological orders on the lattice with parity and time-reversal invariance, arise as magnetic and electric projections of the extended models. We conjecture that all string-net models can be extended in an analogous way, using a more general algebraic structure, such that EM duality continues to hold. Physical applications include topology probes in the form of pairs of dual tensor networks.
Aguado Miguel
Buerschaper Oliver
Christandl Matthias
Kong Liang
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