Bosonic resonating valence bond theory of the possible chiral spin-liquid state in the triangular-lattice Hubbard model

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