Anyons in a highly-entangled toric xy model

While ostensibly coined in 1989 by Xiao-Gang Wen, the term “topological order” has been in use since 1972 by Kosterlitz–Thouless to describe the behavior of the classical xy model. It has been noted that the xy model does not have Wen’s topological order since it is also subject a nontopological \(U(1)\) gauge action. We show in a sense this is the only obstruction. That is, if the xy model evolves quantumly into gauge invariant states then one recovers pure topological order. In fact, we show the quantum xy topological order is an infinite lattice limit of Kitaev’s quantum double model applied to the group \(G = \mathbb{Z}\).

Preprint is available here.