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arXiv:2211.02031 · Physical review. B./Physical review. B

Spectral properties of a one-dimensional extended Hubbard model from bosonization and time-dependent variational principle: Applications to one-dimensional cuprates

Hao-Xin Wang, Yiming Wu, Yi‐Fan Jiang, Hong Yao

Published Jan 2, 2024• 20 citations
arXivHTMLPDF

Abstract

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 $U$ and nearest-neighbor interaction $V$, 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 $3{k}_{F}$ branches evolve oppositely as a function of $V$, and a moderate attractive $V$ 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 $3{k}_{F}$ 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.

DOI
10.1103/physrevb.109.045102

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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.
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.
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.
Quasi-one-dimensional (1D) materials provide a unique platform for understanding the importance and influence of extended interactions on the physics of strongly correlated systems due to their relative structural simplicity and the existence of powerful theoretical tools well adapted to one spatial dimension. Recently, this was highlighted by anomalous observations in the single-particle spectral function $A(q,\ensuremath{\omega})$ of 1D cuprate chain compounds, measured by angle-resolved photoemission spectroscopy (ARPES), which were explained by the presence of a long-range attractive interaction. Such an extended interaction should leave its fingerprints on other observables, notably the dynamical spin structure factor $S(q,\ensuremath{\omega})$, measured by neutron scattering or resonant inelastic x-ray scattering. Starting from a simple Hubbard Hamiltonian in 1D and using time-dependent density matrix renormalization group methods, we show that the presence of long-range attractive coupling, directly through an instantaneous Coulomb interaction VVV or retarded electron-phonon (el-ph) coupling, can introduce significant spectral weight redistribution in $S(q,\ensuremath{\omega})$ across a wide range of doping. This underscores the significant impact that extended interactions can have on dynamical correlations among particles, and the importance of properly incorporating this influence in modeling. Our results demonstrate that $S(q,\ensuremath{\omega})$ can provide a sensitive experimental constraint, which complements ARPES measurements, in identifying key interactions in 1D cuprates, beyond the standard Hubbard model.
Recent angle-resolved photoemission spectroscopy (ARPES) for a newly discovered doped one-dimensional (1D) Mott insulator ${\mathrm{Ba}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{3+\ensuremath{\delta}}$ proposed the presence of attractive charge interactions between neighboring sites if a 1D Hubbard model is employed to describe the material. On the other hand, long-range repulsive charge interactions were proposed to be crucial for understanding the optical excitations of undoped 1D Mott insulators. Motivated by these contrasting proposals, we perform density-matrix renormalization group calculations of the single-particle spectral function as well as dynamical spin and charge structure factors for two kinds of extended 1D Hubbard models. The spectral function for the long-range repulsive model less agrees with the ARPES data as compared with that for the attractive one. The dynamical spin and charge structure factors also exhibit contrasting behaviors between the two models: The attractive model shows less momentum dependence of the integrated weight in the dynamical spin structure factor and more accumulation of the weight on the upper edge of particle-hole-type excitation in the dynamical charge structure factor. These features give a good criterion of an appropriate model for doped 1D Mott insulators, which can be judged by resonant-inelastic x-ray scattering experiments.
We consider a multiband Hubbard model Hm{H}_{m}Hm​ 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 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.