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arXiv:1006.1388

Bethe-Salpeter equations for the collective modes of the $t-U-V-J$ model with d-wave pairing

Zlatko G. Koinov, Patrick L. Nash

Published Jun 7, 2010• 0 citations
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Abstract

The Bethe-Salpeter equations for the collective modes of a $t$-$U$-$V$-$J$ model are used to analyze the resonance peak observed at $\bf{Q}=(π,π)$ in neutron scattering experiments on the cuprates. We assume that the resonance emerges due to the mixing between the spin channel and 19 other channels. We have calculated the energy of the lowest mode of the extended Hubbard model ($J=0$) vs the on-site repulsive interaction $U$, as well as the $UJ$ lines in the interaction parameter space which are consistent with the ARPES data and reproduces the resonance peak at 40 meV in Bi2212 compound. We find that the resonance is predominantly a spin exciton.

DOI
10.48550/arxiv.1006.1388

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Bethe-Salpeter equations for the collective modes of the t−U−V−Jt-U-V-Jt−U−V−J model with d-wave pairing
The Bethe-Salpeter equations for the collective modes of a ttt-UUU-VVV-JJJ model are used to analyze the resonance peak observed at Q=(π,π)\bf{Q}=(π,π)Q=(π,π) in neutron scattering experiments on the cuprates. We assume that the resonance emerges due to the mixing between the spin channel and 19 other channels. We have calculated the energy of the lowest mode of the extended Hubbard model (J=0J=0J=0) vs the on-site repulsive interaction UUU, as well as the UJUJUJ lines in the interaction parameter space which are consistent with the ARPES data and reproduces the resonance peak at 40 meV in Bi2212 compound. We find that the resonance is predominantly a spin exciton.
The Bethe-Salpeter equations for the collective modes of a $t\text{\ensuremath{-}}U\text{\ensuremath{-}}V\text{\ensuremath{-}}J$ model are used to analyze the resonance peak observed at $\mathbf{Q}=(\ensuremath{\pi},\ensuremath{\pi})$ in neutron-scattering experiments on the cuprates. We assume that the resonance emerges due to the mixing between the spin channel and 19 other channels. We have calculated the energy of the lowest mode of the extended Hubbard model (J=0)(J=0)(J=0) vs the on-site repulsive interaction UUU, as well as the UJUJUJ lines in the interaction parameter space which are consistent with the angle-resolved photoemission spectroscopy data and reproduces the resonance peak at 40 meV in Bi2212 compound. We find that the resonance is predominantly a spin exciton.
The Bethe-Salpeter equation is combined with the temperature-cutoff functional renormalization group approach to analyze the order parameter structure for the leading instabilities of the 2D $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}$ Hubbard model. We find significant deviations from the conventional sss-, ppp-, or ddd-wave forms, which is due to the frustration of antiferromagnetism at small and intermediate ${t}^{\ensuremath{'}}$. With adding a direct antiferromagnetic spin-exchange coupling the eigenfunctions in the particle-hole channel have extended sss-wave form, while in the particle-particle singlet pairing channel a higher angular momentum component arises besides the standard ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ wave component, which flattens the angular dependence of the gap. For ${t}^{\ensuremath{'}}$ closer to t∕2t∕2t∕2 we find a delicate competition of ferromagnetism and triplet pairing with a nontrivial pair-wavefunction.
We provide a unified interpretation of both paramagnon and plasmon modes in high-Tc{T}_{c}Tc​ copper-oxides, and verify it quantitatively against available resonant inelastic xxx-ray scattering (RIXS) data across the hole-doped phase diagram. The three-dimensional extended Hubbard model, with included long-range Coulomb interactions and doping-independent microscopic parameters for both classes of quantum fluctuations, is used. Collective modes are studied using VWF+1/Nf\mathrm{VWF}+1/{\mathcal{N}}_{f}VWF+1/Nf​ approach which extends variational wave function (VWF) scheme by means of an expansion in inverse number of fermionic flavors (1/Nf)(1/{\mathcal{N}}_{f})(1/Nf​). We show that intense paramagnons persist along the antinodal line from the underdoped to the overdoped regime and undergo rapid overdamping in the nodal direction. Plasmons exhibit a three-dimensional character, with minimal energy corresponding to antiphase oscillations on neighboring CuO2{\mathrm{CuO}}_{2}CuO2​ planes. The theoretical spin- and charge excitation energies reproduce semiquantitatively RIXS data for ${(\mathrm{Bi},\mathrm{Pb})}_{2}{(\mathrm{Sr},\mathrm{La})}_{2}{\mathrm{CuO}}_{6+\ensuremath{\delta}}$. The present VWF+1/Nf\mathrm{VWF}+1/{\mathcal{N}}_{f}VWF+1/Nf​ analysis of dynamics and former VWF results for static quantities combine into a consistent description of the principal properties of hole-doped high-Tc{T}_{c}Tc​ cuprates as strongly correlated systems.
The t-J-U model of high-Tc copper-oxide superconductors incorporates both the on-site Coulomb repulsion and kinetic exchange interaction and yields a semi-quantitative description of the static properties of those materials. We extend this analysis to dynamic quantities and address collective spin- and charge excitations in the correlated metallic state of the t-J-U model. We employ VWF+1/Nf approach that combines the variational wave function (VWF) approach with the expansion in the inverse number of fermionic flavors (1/Nf). It is shown that the resonant (paramagnon) contribution to the dynamic magnetic susceptibility remains robust as one interpolates between the Hubbard- and t-J-model limits, whereas the incoherent continuum undergoes substantial renormalization. Energy of the collective charge mode diminishes as the strong-coupling limit is approached. We also introduce the concept of effective kinetic exchange interaction that allows for a unified interpretation of magnetic dynamics in the Hubbard, t-J, and t-J-U models. The results are discussed in the context of recent resonant inelastic x-ray scattering experiments for the high-Tc cuprates.
We study the three-band Hubbard model for the copper oxide plane of the high-temperature superconducting cuprates using determinant quantum Monte Carlo and the dynamical cluster approximation (DCA) and provide a comprehensive view of the pairing correlations in this model using these methods. Specifically, we compute the pair-field susceptibility and study its dependence on temperature, doping, interaction strength, and charge-transfer energy. Using the DCA, we also solve the Bethe-Salpeter equation for the two-particle Green's function in the particle-particle channel to determine the transition temperature to the superconducting phase on smaller clusters. Our calculations reproduce many aspects of the cuprate phase diagram and indicate that there is an ``optimal'' value of the charge-transfer energy for the model where Tc{T}_{c}Tc​ is largest. These results have implications for our understanding of superconductivity in both the cuprates and other doped charge-transfer insulators.
A Bethe-Salpeter equation is obtained by using of the $t\ensuremath{-}J$ Hamiltonians that satisfy the U(1) and the SU(2) slave-boson symmetries, respectively. Holon-holon scattering channels in the Bethe-Salpeter equation are judiciously examined at a critical temperature to study the instability of the normal state against holon pairing. From the present study of the holon pairing instability, an arch-shaped bose condensation line is revealed in agreement with the observation for high-Tc{T}_{c}Tc​ cuprates over a range of hole doping concentration.