Hubbard model on a triangular lattice: The role of charge fluctuations

A chiral spin liquid (CSL) phase has been recently reported in the Hubbard model on a triangular lattice. It emerges in an intermediate coupling regime at half-filling, which is sandwiched between a 120^ antiferromagnetic (AFM) phase and a metallic phase as a function of on-site repulsion U. In this work, we examine the mechanism of the CSL and complex phase diagram via analytic analysis and numerical density matrix renormalization group (DMRG) method. First, we identify an exact Berry-phase-like sign structure in the partition function of the model at arbitrary U, which is originated from the Fermi sign structure at U=0. The spin and charge degrees of freedom are generally entangled via a singular phase string in such a many-body sign structure. In the large-U limit, the suppression of the charge fluctuation at half-filling can render the phase string ineffective, resulting in the AFM order. However, if one precisely switches off such a phase string in the DMRG calculation, the 120^ AFM is shown to survive all the way down to a much weaker U without the emergence of the CSL and metallic phases. It indicates that the phase-string sign structure plays the key role to mediate the mutual interaction between the charge and spin fluctuations, which results in the CSL and metallic phases at finite U. General implications for the Mott physics in the Hubbard model will also be discussed.