Electric-magnetic duality of lattice systems with topological order

Understand

We investigate the duality structure of quantum lattice systems with topological order, a collective order also appearing in fractional quantum Hall systems.

• We define electromagnetic (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 intrinsic 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 more general algebraic and tensor-categorical structures, such that EM duality continues to hold.