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arXiv:cond-mat/9610200 · Journal of the Physical Society of Japan

Superconductivity in the Three-Leg Hubbard Ladder: A Quantum Monte Carlo Study

Takashi Kimura, Kazuhiko Kuroki, Hideo Aoki

Published Jun 15, 1997• 10 citations
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Abstract

Quantum Monte Carlo method is used to look into the superconductivity in the three-leg Hubbard ladder. The enhanced correlation for the pairing across the central and edge chains, which has been predicted in the weak-coupling renormalization as an effect of coexistence of gapful and gapless spin modes, is here shown to persist for intermediate interaction strengths.

DOI
10.1143/jpsj.66.1599

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Quantum Monte Carlo method is used to look into the superconductivity in the three-leg Hubbard ladder. The enhanced correlation for the pairing across the central and edge chains, which has been predicted in the weak-coupling renormalization as an effect of coexistence of gapful and gapless spin modes, is here shown to persist for intermediate interaction strengths.
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An extensive quantum Monte Carlo calculation is performed for the two-leg Hubbard ladder model to clarify whether the singlet pairing correlation decays slowly, which is predicted from the weak-coupling theory but controversial from numerical studies. Our result suggests that the discreteness of energy levels in finite systems affects the correlation enormously, where the enhanced pairing correlation is indeed detected if we make the energy levels of the bonding and antibonding bands lie close to each other at the Fermi level to mimic the thermodynamic limit.
In order to check whether odd-numbered Tomonaga-Luttinger ladders are dominated by antiferromagnetic correlations associated with gapless spin excitations, correlation functions of the doped three-chain Hubbard model are obtained with the bosonization at the renormalization-group fixed point. The correlation of the singlet superconducting pairing across the central and edge chains is found to be dominant, reflecting two gapful spin modes, while the intraedge spin-density-wave correlation, reflecting the gapless mode, is only subdominant. This implies that, when there are multiple spin modes, a dominant superconductivity can arise from the presence of some spin gap(s) despite the coexistence of power-law correlated spins.
In the ground state of the doped two-leg Hubbard ladder there are power-law decaying d_{x^2-y^2}-type pairing correlations. It is important to know the strength and the temperature scale of these correlations. For this purpose, we have performed determinantal Quantum Monte Carlo (QMC) calculations of the reducible particle-particle interaction in the Hubbard ladder. In this paper, we report on these calculations and show that, at sufficiently low temperatures, resonant particle-particle scattering takes place in the d_{x^2-y^2} pairing channel for certain values of the model parameters. The QMC data presented here indicate that the d_{x^2-y^2} pairing correlations are strong in the Hubbard ladder.
Monte Carlo calculations of the irreducible particle-particle interaction on a two-leg Hubbard ladder doped near half-filling are reported. As the temperature is lowered, this interaction develops structure in momentum space similar to the magnetic susceptibility χ(q)χ(q)χ(q) and reflects the development of strong short-range antiferromagnetic correlations. Using this interaction, the eigenfunction of the leading singlet pair eigenvalue is found to have dx2−y2d_{x^2-y^2}dx2−y2​ like symmetry. The single-particle spectral weight is also shown to peak near (π,0)(π,0)(π,0) and (0,π)(0,π)(0,π) when the ratio of the inter- to intra-chain hopping t⊥/t≃1.5t_{\perp}/t\simeq 1.5t⊥​/t≃1.5, leading to an increased tendency for pairing.
We study signatures of superconductivity in a two-leg ``checkerboard'' Hubbard ladder model, defined as a one-dimensional (period 2) array of square plaquettes with an intraplaquette hopping ttt and interplaquette hopping ${t}^{\ensuremath{'}}$, using the density-matrix renormalization-group method. The highest pairing scale (characterized by the spin gap or the pair binding energy, extrapolated to the thermodynamic limit) is found for doping levels close to half-filling, $U\ensuremath{\approx}6t$ and ${t}^{\ensuremath{'}}/t\ensuremath{\approx}0.6$. Other forms of modulated hopping parameters, with periods of either one or three lattice constants, are also found to enhance pairing relative to the uniform two-leg ladder, although to a lesser degree. A calculation of the phase stiffness of the ladder reveals that in the regime with the strongest pairing, the energy scale associated with phase ordering is comparable to the pairing scale.