Geometry and topological order in the non-relativistic Luttinger liquid
  We demonstrate that the notion of spin-charge separation as follows from the Tomonaga-Luttinger theory of relativistic fermions does not suffice to completely specify the Luttinger liquid state associated with the fermions of condensed matter physics. The latter carries in addition a form of topological order which can be made visible using non-local correlation functions familiar from lattice gauge theory. 
H.V. Kruis, I.P. McCulloch, Z. Nussinov and J. Zaanen