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arXiv:cond-mat/9612166

Monte Carlo study of the pairing interaction in the two-leg Hubbard ladder

Bulut, N., T. Dahm, Douglas J. Scalapino

Published Dec 18, 1996• 0 citations
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Abstract

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 $χ(q)$ 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 $d_{x^2-y^2}$ like symmetry. The single-particle spectral weight is also shown to peak near $(π,0)$ and $(0,π)$ when the ratio of the inter- to intra-chain hopping $t_{\perp}/t\simeq 1.5$, leading to an increased tendency for pairing.

DOI
10.48550/arxiv.cond-mat/9612166

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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.
Here we discuss Quantum Monte Carlo results for the magnetic susceptibility, single-particle spectral weight and the irreducible particle-particle interaction vertex of the two-dimensional Hubbard model. In the doped system, as the temperature is lowered below J=4t^2/U, short-range antiferromagnetic correlations develop. These lead to a narrow low-energy quasiparticle band with a large Fermi surface and a particle-particle vertex which increases at large momentum transfer, which favor d_{x^2-y^2}-pairing.
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.
A dynamic cluster quantum Monte Carlo approximation is used to study the effective pairing interaction of a two-dimensional Hubbard model with a near neighbor hopping ttt and an onsite Coulomb interaction UUU. The effective pairing interaction is characterized in terms of the momentum and frequency dependence of the eigenfunction of the leading eigenvalue of the irreducible particle-particle vertex. The momentum dependence of this eigenfunction is found to vary as (coskx−−cosky)(\mathrm{cos}\phantom{\rule{0.2em}{0ex}}{k}_{x}--\mathrm{cos}\phantom{\rule{0.2em}{0ex}}{k}_{y})(coskx​−−cosky​) over most of the Brillouin zone and its frequency dependence is determined by the S=1S=1S=1 particle-hole continuum which for large UUU varies as several times JJJ. This implies that the effective pairing interaction is attractive for singlets formed between near-neighbor sites and retarded on a time scale set by ${(2J)}^{\ensuremath{-}1}$. The strength of the pairing interaction measured by the size of the ddd-wave eigenvalue peaks for UUU of order of the bandwidth 8t8t8t. It is found to increase as the system is underdoped.
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.
A dynamic cluster quantum Monte Carlo approximation is used to study the effective pairing interaction of a 2D Hubbard model with a near neighbor hopping ttt and an on-site Coulomb interaction UUU . The effective pairing interaction is characterized in terms of the momentum and frequency dependence of the eigenfunction of the leading eigenvalue of the irreducible particle-particle vertex. The momentum dependence of this eigenfunction is found to vary as (cos⁡kx−cos⁡ky)(\cos k_x-\cos k_y)(coskx​−cosky​) over most of the Brillouin zone and its frequency dependence is determined by the exchange energy JJJ. This implies that the effective pairing interaction is attractive for singlets formed between near-neighbor sites and retarded on a time scale set by J−1J^{-1}J−1. The strength of the pairing interaction measured by the size of the d-wave eigenvalue peaks for UUU of order the bandwidth 8t8t8t. It is found to increase as the system is underdoped.