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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 γ as a tool, we establish topological order in chiral spin liquid and Z2 spin liquid wave-functions, as well as a lattice version of the Laughlin state. Our results agree very well with the field theoretic result γ=log D where D is the total quantum dimension of the phase. All calculations are done using a Monte Carlo technique on a 12 times 12 lattice enabling us to extract γ 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 ν=1/3 phase with the expected γ=log \sqrt{3}.