Pairing correlation in the three-leg Hubbard ladder - Renormalization group and quantum Monte Carlo studies

In order to investigate the validity of a conjecture that correlated electrons in ladders having even-numbered legs exhibit superconductivity accompanied by a spin gap while odd ones do not, the pairing correlation is studied for the three-leg ladder in the Hubbard model. Both the renormalization group for weak interactions and the quantum Monte Carlo (QMC) method for strong interactions are employed. The weak-coupling study predicts that the superconducting correlation dominates, which refutes the naive even-odd conjecture. A crucial point is that a spin gap for only some out of multiple spin modes can suffice to make the ladder superconduct with a pairing symmetry (d-like here) compatible with the gapped mode. A QMC study endorses the enhanced pairing correlation for stronger Hubbard repulsions. Effects of Umklapp processes are also elucidated. A small energy scale relevant here requires a care in the QMC related to the discreteness of one-electron levels. This argument is reinforced from the result for an exactly solvable, one-dimensional attractive Hubbard model.