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Pairing correlations in the two-leg Hubbard ladder

Niyazi Bulut, Sadamichi Maekawa

Published Jul 30, 2005• 0 citations
OpenAlex

Abstract

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.

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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.
In the ground state of the doped two-leg Hubbard ladder there are power-law decaying ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-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 ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ pairing channel for certain values of the model parameters. The QMC data presented here indicate that the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ 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.
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.
The numerical studies of d x 2 - y 2 -wave pairing in the two-dimensional (2D) and the 2-leg Hubbard models are reviewed. For this purpose, the results obtained from the determinantal Quantum Monte Carlo and the Density-Matrix Renormalization-Group calculations are presented. These are calculations which were motivated by the discovery of the high- T c cuprates. In this review, the emphasis is placed on the microscopic many-body processes which are responsible for the d x 2 - y 2 -wave pairing correlations observed in the 2D and the 2-leg Hubbard models. In order to gain insight into these processes, the results on the effective pairing interaction as well as the magnetic, density and the single-particle excitations will be reviewed. In addition, comparisons will be made with the other numerical approaches to the Hubbard model and the numerical results on the t - J model. The results reviewed here indicate that an effective pairing interaction which is repulsive at ( ~ , ~ ) momentum transfer, and enhanced single-particle spectral weight near the ( ~ ,0) and (0, ~ ) points of the Brillouin zone, create optimum conditions for d x 2 - y 2 -wave pairing. These are two effects which act to enhance the d x 2 - y 2 -wave pairing correlations in the Hubbard model. Finding additional ways is an active research problem.
The two-leg Hubbard ladder is characterized by the ratio of the inter- to intra-leg hopping ${t}_{\ensuremath{\perp}}/t$, the relative interaction strength U/t,U/t,U/t, and the electron filling. Here, using density matrix renormalization group and Monte Carlo simulations, we examine the dependence of the pairing correlations on these parameters. We find that the pairing correlations are enhanced when the top of the bonding quasiparticle band and the bottom of the antibonding band are near the Fermi level. We present results on the single-particle spectral weight and the antiferromagnetic correlations in order to explain this behavior.