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 ${120}^{\circ }$ 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 ${120}^{\circ }$ 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.

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• Quantum spin liquid
• Triangular lattice
• Hubbard model
• Lattice models in condensed matter
• Many-body techniques
• Numerical techniques