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arXiv:cond-mat/0312654 · Physical Review B

Charge fluctuations and electron-phonon interaction in the finite- U Hubbard model

E. Cappelluti, Benedetta Cerruti, L. Pietronero

Published Apr 15, 2004• 25 citations
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Abstract

In this paper we employ a Gaussian expansion within the finite-$U$ slave-bosons formalism to investigate the momentum structure of the electron-phonon vertex function in the Hubbard model as function of U and n. The suppression of large momentum scattering and the onset of a small-$\mathbf{q}$ peak structure, parametrized by a cut-off ${q}_{c},$ are shown to be essentially ruled by the band narrowing factor ${Z}_{\mathrm{MF}}$ due to the electronic correlation. A phase diagram of ${Z}_{\mathrm{MF}}$ and ${q}_{c}$ in the whole $U--n$ space is presented. Our results are in more than qualitative agreement with a recent numerical analysis and permit one to understand some anomalous features of the quantum Monte Carlo data.

DOI
10.1103/physrevb.69.161101

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The renormalization of the electron-phonon interaction by strong electronic correlations is studied using a one-band Hubbard model with infinite repulsion and nearest (t model) and nearest and second-nearest (tt\ensuremath{'} model) neighbor hopping terms and an on-site electron-phonon coupling. Using Hubbard's X operators and an extension from 2 to N degrees of freedom for the electrons the leading contributions for the electron self-energy and the vertex function in 1/N and the electron-phonon coupling constant are given and numerically evaluated for a square lattice. We find that the momentum dependence of the vertex function depends strongly on doping: For large dopings it is rather weak, with decreasing doping it becomes more and more pronounced leading to a strong reduction of the vertex at larger momentum transfers until, for very small dopings, the vertex essentially consists of a forward scattering peak with a width proportional to the doping. This behavior occurs both in the t and the tt\ensuremath{'} models and also in one dimension where analytic expressions are derived. Correlation effects also change ${\mathrm{\ensuremath{\alpha}}}^{2}$F in general: The full-symmetric component ${\mathrm{\ensuremath{\alpha}}}^{2}$F1{\mathit{F}}_{1}F1​ is in the t model somewhat, in the tt\ensuremath{'} model rather strongly suppressed, especially near half-filling; the other symmetry components ${\mathrm{\ensuremath{\alpha}}}^{2}$Fi{\mathit{F}}_{\mathit{i}}Fi​ with i=2,...,5 increase strongly with decreasing doping and are of similar magnitude as ${\mathrm{\ensuremath{\alpha}}}^{2}$F1{\mathit{F}}_{1}F1​ near half-filling.Including also direct Coulomb repulsion nontrivial symmetries such as d wave become more stable than the s-wave order parameter below a critical value for the doping even for the considered phonon-mediated superconductivity. Most dramatic, however, is the quenching of the resistivity due to electron-phonon scattering both in the t and the tt\ensuremath{'} models at intermediate and small dopings. This result may explain the absence of phonon features in the experimental transport coefficients of high-Tc{\mathit{T}}_{\mathit{c}}Tc​ compounds. \textcopyright{} 1996 The American Physical Society.
We investigate the effect of electronic correlations on the coupling of electrons to Holstein phonons in the one-band Hubbard model. We calculate the static electron-phonon vertex within the linear response of Kotliar-Ruckenstein slave bosons in the paramagnetic saddle-point approximation. Within this approach the on-site Coulomb interaction UUU strongly suppresses the coupling to Holstein phonons at low temperatures. Moreover, the vertex function does not show particularly strong forward scattering. Going to larger temperatures $kT\ensuremath{\sim}t$ we find that after an initial decrease with UUU, the electron-phonon coupling starts to increase with UUU, confirming a recent result of Cerruti, Cappelluti, and Pietronero. We show that this behavior is related to an unusual reentrant behavior from a phase separated to a paramagnetic state upon decreasing the temperature.
Abstract Several state-of-the-art numerical methods have observed static or fluctuating spin and charge stripes in doped two-dimensional Hubbard models, suggesting that these orders play a significant role in shaping the cuprate phase diagram. Many experiments, however, also indicate that the cuprates have strong electron-phonon (e-ph) coupling, and it is unclear how this interaction influences stripe correlations. We study static and fluctuating stripe orders in the doped single-band Hubbard-Holstein model using zero temperature variational Monte Carlo and finite temperature determinant quantum Monte Carlo. We find that the lattice couples more strongly with the charge component of the stripes, leading to an enhancement or suppression of stripe correlations, depending on model parameters like the next-nearest-neighbor hopping t′{t}^{{\prime} }t′ t′ or phonon energy Ω. Our results help elucidate how thee-ph interaction can tip the delicate balance between stripe and superconducting correlations in the Hubbard-Holstein model with implications for our understanding of the high-Tccuprates.