Discrete non-Abelian gauge theories in two-dimensional lattices and their realizations in Josephson-junction arrays

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  • 5 February 2003
Abstract
We discuss real space lattice models equivalent to gauge theories with a discrete non-Abelian gauge group. We contruct the Hamiltonian formalism which is appropriate for their Solid State Physics implementation and we outline their basic properties. The unusual physics of these systems is due to local constraints on the degrees of freedom which are variables localized on the links of the lattice. We discuss two types of constraints that become equivalent after a duality transformation for Abelian theories but are qualitatively different for non-Abelian ones. We emphasize highly nontrivial topological properties of the excitations (fluxons and charges) in these non-Abelian discrete lattice gauge theories and their possible use for quantum computation. We suggest a few designs of Josephson-junction arrays that provide experimental realizations of these models and discuss the physical restrictions on the parameters of their junctions.

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