Symmetric Z₂ spin liquids and their neighboring phases on triangular lattice

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Motivated by recent numerical discovery of a gapped spin liquid phase in spin-1/2 triangular-lattice J₁-J₂ Heisenberg model, we classify symmetric Z₂ spin liquids on triangular lattice in the Abrikosov-fermion representation. We find 20 phases with distinct spinon symmetry quantum numbers, 8 of which have their counterparts in the Schwinger-boson representation. Among them we identify 2 promising candidates (#1 and #20), which can realize a gapped Z₂ spin liquid with up to next nearest neighbor mean-field amplitudes. We analyze their neighboring magnetic orders and valence bond solid patterns, and find one state (#20) that is connected to 120-degree Neel order by a continuous quantum phase transition. We also identify gapped nematic Z₂ spin liquids in the neighborhood of the symmetric states and find 3 promising candidates (#1, #6 and #20).