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EPJ Web of Conferences

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

N. Bulut

Published Jan 1, 2012• 0 citations
Publisher

Abstract

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.

DOI
10.1051/epjconf/20122300006

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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.
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.
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.
We report the results of zero-temperature quantum Monte Carlo simulations and zero-temperature mean-field calculations of the attractive Hubbard model on chains, ladders, and square lattices. We investigated the predictability of the BCS approximation, the dimensional crossover of the pairing correlation function from one to two dimensions as a function of the ladder width, and the scaling of these correlations to the thermodynamic limit of the two-dimensional model. We found that the BCS wave function is quantitatively correct only for small values of U/t.U/t.U/t. For the system sizes, electron fillings, and interaction strengths studied, we never saw the dimensional crossover. In general, our ability to achieve the dimensional crossover and accurate scaling to the thermodynamic limit was limited by the size of the systems we could simulate. For these sizes, although we saw the necessary signature of off-diagonal long-range order, the properties of the model did not vary monotonically with increasing system size because of shell effects. We contrast this situation with the dimensional crossover and scaling to the thermodynamic limit of the Ising model.
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.
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.
The irreducible particle-particle interaction ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{I}}$ of the two-dimensional Hubbard model is calculated by quantum Monte Carlo simulations. The Bethe-Salpeter equation for the pair-wave function is then solved using the Monte Carlo data for ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{I}}$ and the single-particle Green's function. The dominant pairing correlations in the intermediate-coupling regime and at small dopings are discussed.