Hubbard Model on Triangular Lattice: Role of Charge Fluctuations

A chiral spin liquid (CSL) phase has been recently reported in the Hubbard model on a triangular lattice at half-filling. It emerges in an intermediate coupling regime, which is sandwiched between a $120^\circ$ antiferromagnetic (AFM) phase and a metallic phase as a function of on-site repulsion $U$. In this work, we examine how the charge fluctuation may cause the CSL and complex phase diagram. We first identify an exact sign structure of the model at arbitrary temperature, sample size, and doping, which is reduced from the original Fermi exchange signs of the electrons by finite $U$. In particular, the spin and charge degrees of freedom are generally entangled via the phase-string in the sign structure. By precisely switching off such a phase-string, the CSL phase is shown to disappear, with only the $120^\circ$ AFM order remaining down to weak $U$ by a density matrix renormalization group calculation. Here the charge fluctuation is effectively decoupled from the AFM background, which is a $120^\circ$ AFM order due to a geometric Berry phase in the sign structure of the triangular lattice. General implications for the Mott physics will also be discussed.