We investigate the phase diagram of the half-filled triangular-lattice Hubbard model using the density-matrix renormalization group method. By systematically studying the ground-state properties with the ratio of on-site Coulomb repulsion and bandwidth, we first identify two competing intermediate phases in the vicinity of metal-insulator transition on narrow cylinders with width $L_y=3$: a gapped chiral spin liquid phase and a gapless phase with stripy antiferromagnetic quasi-long-range order. Then, as the system width increases to width $L_y=4,6,7$, the spin chirality order persists in a wider range of parameters with significantly enhanced amplitude, giving rise to a robust chiral spin liquid phase toward the two-dimensional limit. The stripy antiferromagnetic quasi-long-range order phase, however, is fragile and eventually disappears. We further extrapolate the amplitude of the spin chirality order parameter as a function of cylinder width and also address the previous discrepancies on the nature of intermediate phases.

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• Strongly correlated systems
• Triangular lattice
• Hubbard model