Local disorder, topological ground state degeneracy and entanglement   entropy, and discrete anyons
  In this comprehensive study of Kitaev's abelian models defined on a graph embedded on a closed orientable surface, we provide complete proofs of the topological ground state degeneracy, the absence of local order parameters, compute the entanglement entropy exactly and characterise the elementary anyonic excitations. The homology and cohomolgy groups of the cell complex play a central role and allow for a rigorous understanding of the relations between the above characterisations of topological order. 
Sven Bachmann
math-ph cond-mat.stat-mech math.MP