Gapless spin liquid and pair density wave of the Hubbard model on three-leg triangular cylinders

We study the ground state properties of 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 at weak coupling and Mott insulating dimer strong interaction, which has one mode algebraic spin-spin correlations but exponential decay scalar chiral-chiral correlations. Upon light doping liquid, system exhibits power-law charge-density-wave (CDW) short-range single-particle, spin-spin, Similar to CDW correlations, superconducting are also quasi-long-ranged oscillate in sign as function distance, is consistent with striped pair-density wave. When further or order phase, another takes over, similar all other exponentially.