Testing for topological order in variational wavefunctions for Z(2) spin liquids

Abstract

We determine the conditions under which a spin-liquid Mott insulator |0> defined by a Gutzwiller projected BCS state at half-filling is Z(2) fractionalized. We construct a trial vison [Z(2) vortex] state |V> by projecting an (hc/2e) vortex threading the hole of a cylinder/torus and examine its overlap with |0> using analytical and numerical calculations. We find that generically the overlap vanishes in the thermodynamic limit, so the spin-liquid is Z(2) fractionalized. We point out the relevance of these results to numerical studies of Hubbard-like models and spin models which have been recently reported to possess spin liquid phases. We also consider possible implications for flux-trapping experiments that have tested for Z(2) fractionalization in underdoped high temperature superconductors.