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arXiv:2303.11905 · Physical review. B./Physical review. B

Effective one-band models for the one-dimensional cuprate Ba2−xSrxCuO3+δ

Adrian E. Feiguin, Christian Helman, Armando A. Aligia

Published Aug 9, 2023• 8 citations
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Abstract

We consider a multiband Hubbard model ${H}_{m}$ for Cu and O orbitals in ${\mathrm{Ba}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{3+\ensuremath{\delta}}$ similar to the three-band model for two-dimensional cuprates. The hopping parameters are obtained from maximally localized Wannier functions derived from ab initio calculations. Using the cell perturbation method, we derive both a generalized $t\text{\ensuremath{-}}J$ model ${H}_{tJ}$ and a one-band Hubbard model ${H}_{H}$ to describe the low-energy physics of the system. ${H}_{tJ}$ has the advantage of having a smaller relevant Hilbert space, facilitating numerical calculations, while additional terms should be included in ${H}_{H}$ to accurately describe the multiband physics of ${H}_{m}$. Using ${H}_{tJ}$ and the density matrix renormalization group method, we calculate the wave-vector-resolved photoemission and discuss the relevant features in comparison with recent experiments. In agreement with previous calculations, we find that the addition of an attractive nearest-neighbor interaction of the order of the nearest-neighbor hopping shifts the weight from the $3{k}_{F}$ to the holon-folding branch. Kinetic effects also contribute to this process.

DOI
10.1103/physrevb.108.075125

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We consider a multiband Hubbard model Hm{H}_{m}Hm​ for Cu and O orbitals in Ba2\ensuremath−xSrxCuO3+\ensuremathδ{\mathrm{Ba}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{3+\ensuremath{\delta}}Ba2\ensuremath−x​Srx​CuO3+\ensuremathδ​ similar to the three-band model for two-dimensional cuprates. The hopping parameters are obtained from maximally localized Wannier functions derived from ab initio calculations. Using the cell perturbation method, we derive both a generalized t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model HtJ{H}_{tJ}HtJ​ and a one-band Hubbard model HH{H}_{H}HH​ to describe the low-energy physics of the system. HtJ{H}_{tJ}HtJ​ has the advantage of having a smaller relevant Hilbert space, facilitating numerical calculations, while additional terms should be included in HH{H}_{H}HH​ to accurately describe the multiband physics of Hm{H}_{m}Hm​. Using HtJ{H}_{tJ}HtJ​ and the density matrix renormalization group method, we calculate the wave-vector-resolved photoemission and discuss the relevant features in comparison with recent experiments. In agreement with previous calculations, we find that the addition of an attractive nearest-neighbor interaction of the order of the nearest-neighbor hopping shifts the weight from the 3kF3{k}_{F}3kF​ to the holon-folding branch. Kinetic effects also contribute to this process.
We perform a low-energy reduction of the three-band Hubbard Hamiltonian (H3b{\mathit{H}}_{3\mathit{b}}H3b​), keeping in the relevant Hilbert subspace not only local singlets (Zhang-Rice singlets), but also triplet states between Cu holes and O holes at the Wannier function of the same site, with x2{\mathit{x}}^{2}x2-y2{\mathit{y}}^{2}y2 symmetry. We solve exactly the resulting Hamiltonian HT{\mathit{H}}_{\mathit{T}}HT​ in a system of 2\ifmmode\times\else\texttimes\fi{}2 unit cells. From the analytical dependence of the parameters of HT{\mathit{H}}_{\mathit{T}}HT​ and the numerical results, one can see that the local triplet states can be practically neglected for finite O-Cu on-site energy difference \ensuremath{\Delta}, very large Cu on-site Coulomb repulsion Ud{\mathit{U}}_{\mathit{d}}Ud​, and O-O hopping tpp{\mathit{t}}_{\mathit{p}\mathit{p}}tpp​=0. This fact is in contrast with the mapping of H3b{\mathit{H}}_{3\mathit{b}}H3b​ to a one-band model using nonorthogonal singlets, which is very accurate when the Cu+{\mathrm{Cu}}^{+}Cu+ configuration can be neglected. Although the amount of local triplet states in the low-energy eigenstates is in general small, it increases with tpp{\mathit{t}}_{\mathit{p}\mathit{p}}tpp​ and for large tpp{\mathit{t}}_{\mathit{p}\mathit{p}}tpp​ it is necessary to introduce higher-order corrections in the one-band model to accurately represent the low-energy physics. In all cases even when local triplets are not important, the t-J model should be supplemented with other terms, to describe the lowest-energy levels. We also discuss briefly the effect of nonbonding O orbitals.
The appearance of certain spectral features in one-dimensional (1D) cuprate materials has been attributed to a strong, extended attractive coupling between electrons. Here, using time-dependent density matrix renormalization group methods on a Hubbard-extended Holstein model, we show that extended electron-phonon ({\it e-ph}) coupling presents an obvious choice to produce such an attractive interaction that reproduces the observed spectral features and doping dependence seen in angle-resolved photoemission experiments: diminished 3kF3k_F3kF​ spectral weight, prominent spectral intensity of a holon-folding branch, and the correct holon band width. While extended {\it e-ph} coupling does not qualitatively alter the ground state of the 1D system compared to the Hubbard model, it quantitatively enhances the long-range superconducting correlations and suppresses spin correlations. Such an extended {\it e-ph} interaction may be an important missing ingredient in describing the physics of the structurally similar two-dimensional high-temperature superconducting layered cuprates, which may tip the balance between intertwined orders in favor of uniform ddd-wave superconductivity.
Abstract The appearance of certain spectral features in one-dimensional (1D) cuprate materials has been attributed to a strong, extended attractive coupling between electrons. Here, using time-dependent density matrix renormalization group methods on a Hubbard-extended Holstein model, we show that extended electron-phonon (e-ph) coupling presents an obvious choice to produce such an attractive interaction that reproduces the observed spectral features and doping dependence seen in angle-resolved photoemission experiments: diminished 3kF3k_F3kF​ spectral weight, prominent spectral intensity of a holon-folding branch, and the correct holon band width. While extended e-ph coupling does not qualitatively alter the ground state of the 1D system compared to the Hubbard model, it quantitatively enhances the long-range superconducting correlations and suppresses spin correlations. Such an extended e-ph interaction may be an important missing ingredient in describing the physics of the structurally similar two-dimensional high-temperature superconducting layered cuprates, which may tip the balance between intertwined orders in favor of uniform ddd-wave superconductivity.
We calculate the properties of the two-band Hubbard model using the dynamical cluster approximation. The phase diagram resembles the generic phase diagram of the cuprates, showing a strong asymmetry with respect to electron- and hole-doped regimes, in agreement with experiment. Asymmetric features are also seen in one-particle spectral functions and in the charge, spin, and ddd-wave pairing-susceptibility functions. We address the possible reduction of the two-band model to a low-energy single-band one, as it was suggested by Zhang and Rice. Comparing the two-band Hubbard model properties with the single-band Hubbard model ones, we have found similar low-energy physics provided that the next-nearest-neighbor hopping term ${t}^{\ensuremath{'}}$ has a significant value $({t}^{\ensuremath{'}}∕t\ensuremath{\approx}0.3)$. The parameter ${t}^{\ensuremath{'}}$ is the main culprit for the electron-hole asymmetry. However, a significant value of ${t}^{\ensuremath{'}}$ cannot be provided in a strict Zhang and Rice [Phys. Rev. B 37, R3759 (1988); 41, 7243 (1990)] picture where the extra holes added into the system bind to the existing Cu holes forming local singlets. We note that by considering approximate singlet states, such as plaquette states, reasonable values of ${t}^{\ensuremath{'}}$, which capture qualitatively the physics of the two-band model, can be obtained. We conclude that a single-band $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}U$ Hubbard model captures the basic physics of the cuprates concerning superconductivity, antiferromagnetism, pseudogap, and electron-hole asymmetry, but is not suitable for a quantitative analysis or to describe physical properties involving energy scales larger than about 0.5 eV.
Motivated by recent angle-resolved photoemission spectroscopy (ARPES) experiments on doped one-dimensional (1D) cuprates, we investigate spectral properties of a 1D extended Hubbard model with both on-site repulsion UUU and nearest-neighbor interaction VVV, by employing bosonization analysis and the high-precision time-dependent variational principle (TDVP) calculations with large scale up to 300 sites. From state-of-the-art TDVP calculations, we find that the spectral weights of the holon-folding and 3kF3{k}_{F}3kF​ branches evolve oppositely as a function of VVV, and a moderate attractive VVV may best fit the experimental results, hinting at the possible existence of sizable electron-phonon coupling in cuprates. From bosonization analysis, we show that this peculiar dichotomy of holon-folding and 3kF3{k}_{F}3kF​ branches can be explained by a universal relation between the spectral intensity at arbitrary harmonic branches and the Luttinger parameters. We argue that the relation we establish can be used for detecting different interactions in various 1D systems.
Abstract The appearance of certain spectral features in one-dimensional (1D) cuprate materials has been attributed to a strong, extended attractive coupling between electrons. Here, using time-dependent density matrix renormalization group methods on a Hubbard-extended Holstein model, we show that extended electron-phonon (e–ph) coupling presents an obvious choice to produce such an attractive interaction that reproduces the observed spectral features and doping dependence seen in angle-resolved photoemission experiments: diminished 3kF spectral weight, prominent spectral intensity of a holon-folding branch, and the correct holon band width. While extended e–ph coupling does not qualitatively alter the ground state of the 1D system compared to the Hubbard model, it quantitatively enhances the long-range superconducting correlations and suppresses spin correlations. Such an extended e–ph interaction may be an important missing ingredient in describing the physics of the structurally similar two-dimensional high-temperature superconducting layered cuprates, which may tip the balance between intertwined orders in favor of uniform d-wave superconductivity.