Pairing correlation in the two- and three-leg Hubbard ladders --- Renormalization and quantum Monte Carlo studies

TL;DR

This study investigates pairing correlations in two- and three-leg Hubbard ladders using renormalization group and quantum Monte Carlo methods, challenging the traditional even-odd conjecture about superconductivity and spin gaps.

Contribution

It provides evidence that three-leg ladders can exhibit superconductivity despite having an odd number of legs, refuting the naive even-odd conjecture.

Findings

Enhanced pairing correlation in two-leg ladders confirmed by QMC.

Three-leg ladders show dominant superconductivity, contradicting the even-odd conjecture.

Spin gaps in some modes can induce superconductivity with specific pairing symmetry.

Abstract

In order to shed light whether the `even-odd conjecture' (even numbers of legs will superconduct accompanied by a spin gap while odd ones do not) for correlated electrons in ladder systems, the pairing correlation is studied for the Hubbard model on a two- and three-leg ladders. We have employed both the weak-coupling renormalization group and the quantum Monte Carlo (QMC) method for strong interactions. For the two-leg Hubbard ladder, a systematic QMC (with a controlled level spacings) has detected an enhanced pairing correlation, which is consistent with the weak-coupling prediction. We also calculate the correlation functions in the three-leg Hubbard ladder and show that the weak-coupling study predicts the dominant superconductivity, which refutes the naive even-odd conjecture. A crucial point is a spin gap for only some of the multiple spin modes is enough to make the ladder superconduct with a pairing symmetry (d-like here) compatible with the gapped mode. A QMC study for the three-leg ladder endorses the enhanced pairing correlation.