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

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, which has one gapless spin mode and algebraic spin–spin correlations but exponential decay scalar chiral–chiral correlations, between a metallic phase at weak coupling and Mott insulating dimer phase at strong interaction. 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 also decay in power-law 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.