  We study the ground state properties of the Hubbard model on three-leg
triangular cylinders using large-scale density-matrix renormalization group
simulations. At half-filling, we identify an intermediate gapless spin liquid
phase between a metallic phase at weak coupling and Mott insulating dimer phase
at strong interaction, which has one gapless spin mode and algebraic spin-spin
correlations but exponential decay scalar chiral-chiral correlations. Upon
light doping the gapless spin liquid, the system exhibits power-law
charge-density-wave (CDW) correlations but short-range single-particle,
spin-spin, and chiral-chiral correlations. Similar to CDW correlations, the
superconducting correlations are also quasi-long-ranged but oscillate in sign
as a function of distance, which is consistent with the striped pair-density
wave. When further doping the gapless spin liquid phase or doping the dimer
order phase, another phase takes over, which has similar CDW correlations but
all other correlations decay exponentially.

Strongly Correlated Electrons