Anyons in a highly-entangled toric xy model

Abstract

While ostensibly coined in 1989 by Xiao-Gang Wen, the term "topological order" has been in use since 1972 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 non-topological U(1) gauge action. We show in a sense this is the only obstruction. That is, if gauge invariance is enforced energetically then the $xy$ model becomes purely topologically ordered. In fact, we show that the quantum $xy$ topological order is an infinite lattice limit of Kitaev's quantum double model applied to the group G=Z.