Quantum Orders and Spin Liquids in Cs₂CuCl₄

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Motivated by experiments on Cs₂CuCl₄ samples, we studied and classified the symmetric spin liquids on triangular lattice. We identified 63 Z₂ spin liquids, 30 U(1) spin liquids and 2 SU(2) spin liquids. All those spin liquids have the same symmetry but different quantum orders. We calculated the spin spectral functions in some simple spin liquids and compared them to the one measured by experiments on Cs₂CuCl₄. We find that the U1Cτ₊⁰τ₋⁰τ¹ spin liquid or one of its relatives is consistent with observed properties of the spin liquid state in Cs₂CuCl₄. We discussed the fine distinctions among those possible spin liquids and the spin liquids proposed using slave-fermion approach, so that future experiments can determine which spin liquids actually describe the spin state in Cs₂CuCl₄.