Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0508019 · Physical Review B

Strength of dx2−y2 pairing in the two-leg Hubbard ladder

N. Bulut, Sadamichi Maekawa

Published Oct 11, 2006• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.74.132503

Related papers

Pairing correlations in the two-leg Hubbard ladder

Niyazi Bulut, Sadamichi Maekawa

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.

•Jul 30, 2005•0 citations

A simple case ofd(x2-y2) pairing: Hubbard ladder

N. Bulut

We study the strength and the temperature scale of the d(x2-y2) pairing correlations in the Hubbard model on a ladder lattice using Quantum Monte Carlo (QMC) simulations. In particular, we present QMC results on the particle-particle interaction and the solution of the Bethe-Salpeter equation for the d(x2-y2)-wave BCS channel. These data show that there are strong d(x2-y2) pairing correlations in the Hubbard ladder for certain values of the model parameters.

EPJ Web of Conferences•Jan 1, 2012•0 citations

Enhanced dx2−y2 pairing correlations in the two-leg Hubbard ladder

R. M. Noack, N. Bulut, Douglas J. Scalapino +1 more

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 $U/t,$ 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.

arXiv:cond-mat/9612165•Physical review. B, Condensed matter•Sep 15, 1997•94 citations

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

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

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.

arXiv:cond-mat/9612166•Dec 18, 1996•0 citations

Enhancement of the dx2−y2 pairing correlation in the two-dimensional Hubbard model: A quantum Monte Carlo study

Kazuhiko Kuroki, Hideo Aoki

Quantum Monte Carlo is used to investigate the possibility of ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconductivity in the two-dimensional repulsive Hubbard model. A small energy scale relevant to possible pairing requires a care [i.e., sufficiently small level separation between the $k$ points $(\ensuremath{\delta}k,\ensuremath{\pi}\ensuremath{-}\ensuremath{\delta}{k}^{\ensuremath{'}})$ and $(\ensuremath{\pi}\ensuremath{-}\ensuremath{\delta}{k}^{\ensuremath{'}\ensuremath{'}},\ensuremath{\delta}{k}^{\ensuremath{'}\ensuremath{'}\ensuremath{'}})$ with small $\ensuremath{\delta}k$'s] to detect enhanced correlations in finite-size studies, as motivated from a previous study on Hubbard ladders. Our calculation indeed detects long-tailed enhancements in the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ pairing correlation when the system is near, but not exactly at, half-filling.

arXiv:cond-mat/9707277•Physical review. B, Condensed matter•Dec 1, 1997•30 citations

Pairing Correlation in the Three-Leg Hubbard Ladder – Renormalization Group and Quantum Monte Carlo Studies

T. Kimura, Kazuhiko Kuroki, Hideo Aoki

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.

arXiv:cond-mat/9706289•Journal of the Physical Society of Japan•Apr 15, 1998•16 citations
In the ground state of the doped two-leg Hubbard ladder there are power-law decaying dx2\ensuremath−y2{d}_{{x}^{2}\ensuremath{-}{y}^{2}}dx2\ensuremath−y2​-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 dx2\ensuremath−y2{d}_{{x}^{2}\ensuremath{-}{y}^{2}}dx2\ensuremath−y2​ pairing channel for certain values of the model parameters. The QMC data presented here indicate that the dx2\ensuremath−y2{d}_{{x}^{2}\ensuremath{-}{y}^{2}}dx2\ensuremath−y2​ 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-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.
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.
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.
Quantum Monte Carlo is used to investigate the possibility of ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconductivity in the two-dimensional repulsive Hubbard model. A small energy scale relevant to possible pairing requires a care [i.e., sufficiently small level separation between the kkk points $(\ensuremath{\delta}k,\ensuremath{\pi}\ensuremath{-}\ensuremath{\delta}{k}^{\ensuremath{'}})$ and $(\ensuremath{\pi}\ensuremath{-}\ensuremath{\delta}{k}^{\ensuremath{'}\ensuremath{'}},\ensuremath{\delta}{k}^{\ensuremath{'}\ensuremath{'}\ensuremath{'}})$ with small $\ensuremath{\delta}k$'s] to detect enhanced correlations in finite-size studies, as motivated from a previous study on Hubbard ladders. Our calculation indeed detects long-tailed enhancements in the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ pairing correlation when the system is near, but not exactly at, half-filling.
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.