Topological Order in Spin Systems

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Much effort has been devoted to the study of systems with
topological order, motivated by practical issues as well as more field
theoretical and mathematical concerns. This talk will give an overview of some
of the field, describing abelian systems relevant to the search for spin
liquids, and non-abelian systems relevant to topological quantum computation. I
will focus in particular on problems not reducible to free-fermion ones;
examples include the RVB state of electrons as well as models of quantum loops
and nets.