Reexamining doped two-legged Hubbard ladders

We revisit the ground state of the Hubbard model on two-legged ladders in this paper. We perform density matrix renormalization group (DMRG) calculations on large system sizes with large numbers of kept states and perform extrapolation of DMRG results with truncation errors in the converged region. We find that the superconducting correlation exponent Ksc extracted from the pair-pair correlation is very sensitive to the position of the reference bond, reflecting a huge boundary effect on it. By systematically removing the effects from boundary conditions, finite sizes, and truncation errors in DMRG, we obtain more accurate values of Ksc and Kρ with DMRG. With these exponents, we confirm that the two-legged Hubbard model is in the Luther-Emery liquid phase with Ksc·Kρ=1 from tiny doping near half filling to 1/8 hole doping. When the doping is increased to δ⪆1/6, the behaviors of charge, pairing, and spin correlations do not change qualitatively, but the relationship Ksc·Kρ=1 is likely to be violated. With the further increase of the doping to δ=1/3, the quasi-long-ranged charge correlation turns into a true long-ranged charge order, and the spin gap is closed, while the pair-pair correlation still decays algebraically. Our work provides a standard way to analyze the correlation functions when studying systems with open boundary conditions. © 2023 American Physical Society.