  The interplay between spin frustration and charge fluctuation gives rise to
an exotic quantum state in the intermediate-interaction regime of the
half-filled triangular-lattice Hubbard model, while the nature of the state is
under debate. Using the density matrix renormalization group with
SU(2)$_{\rm{spin}} \otimes $U(1)$_{\rm{charge}}$ symmetries implemented, we
study the triangular-lattice Hubbard model defined on the long cylinder
geometry up to circumference $W=6$. A gapped quantum spin liquid, with on-site
interaction $9 \lesssim U / t \lesssim 10.75$, is identified between the
metallic and the antiferromagnetic Mott insulating phases. In particular, we
find that this spin liquid develops a robust long-range spin scalar-chiral
correlation as the system length $L$ increases, which unambiguously unveils the
spontaneous time-reversal symmetry breaking. In addition, the degeneracy of the
entanglement spectrum supports symmetry fractionalization and spinon edge modes
in the obtained ground state. The possible origin of chiral order in this
intermediate spin liquid and its relation to the rotonlike excitations have
also been discussed.
