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

Recent numerical simulations find a possible chiral spin liquid state in the intermediate coupling regime of the triangular lattice Hubbard model. Here we provide 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 be understood as a quantum disordered tetrahedral spin state stabilized by the four spin ring exchange coupling, which suppresses the order-by-disorder effect toward a stripy spin state. Such a chiral spin liquid state features a spin Berry phase of $\frac{\pi}{2}$ per triangle. However, we show that the topological property of such a state is totally missed in the Schwinger Boson mean field description as a result of the lack of Boson rigidity caused by the no double occupancy constraint.