7 research outputs found
Quantum Double Models coupled with matter: an algebraic dualisation approach
In this paper, we constructed a new generalization of a class of discrete
bidimensional models, the so called Quantum Double Models, by introduce matter
qunits to the faces of the lattice that supports these models. This new
generalization can be interpreted as the algebraic dual of a first, where we
introduce matter qunits to the vertices of this same lattice. By evaluating the
algebraic and topological orders of these new models, we prove that, as in the
first generalization, a new phenomenon of quasiparticle confinement may appear
again: this happens when the co-action homomorphism between matter and gauge
groups is non-trivial. Consequently, this homomorphism not only classifies the
different models that belong to this new class, but also suggests that they can
be interpreted as a 2-dimensional restriction of the 2-lattice gauge theories.Comment: 18 pages, 8 figures; submitted to publicatio