Topological entanglement entropy of Z2 spin liquids and lattice Laughlin states

We study entanglement properties of candidate wave functions for SU(2) symmetric gapped spin liquids and Laughlin states. These wave functions are obtained by the Gutzwiller projection technique. Using topological entanglement entropy gamma as a tool, we establish topological order in chiral spin liquid and Z(2) spin liquid wave functions, as well as a lattice version of the Laughlin state. Our results agree very well with the field theoretic result gamma = log D where D is the total quantum dimension of the phase. All calculations are done using a Monte Carlo technique on a 12 x 12 lattice enabling us to extract gamma with small finite-size effects. For a chiral spin liquid wave function, the calculated value is within 4% of the ideal value. We also find good agreement for a lattice version of the Laughlin nu = 1/3 phase with the expected gamma = log root 3.