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Recent numerical simulations find a possible chiral spin liquid state in theintermediate coupling regime of the triangular lattice Hubbard model. Here weprovide a simple picture for its origin in terms of a Bosonic RVB description.More specifically, we show that such a chiral spin liquid state can beunderstood as a quantum disordered tetrahedral spin state stabilized by thefour spin ring exchange coupling, which suppresses the order-by-disorder effecttoward a stripy spin state. Such a chiral spin liquid state features a spinBerry phase of $\frac{\pi}{2}$ per triangle. However, we show that thetopological property of such a state is totally missed in the Schwinger Bosonmean field description as a result of the lack of Boson rigidity caused by theno double occupancy constraint.

On the origin of the possible chiral spin liquid state of the triangular lattice Hubbard model