arXiv:cond-mat/0306131 · Physical review. B, Condensed matter

Electron-phonon vertex in the two-dimensional one-band Hubbard model

Zhongbing Huang, Werner R. Hanke, Enrico Arrigoni, Douglas J. Scalapino

Published Dec 24, 2003• 85 citations

Abstract

Using quantum Monte Carlo techniques, we study the effects of electronic correlations on the effective electron-phonon (el-ph) coupling in a two-dimensional one-band Hubbard model. We consider a momentum-independent bare ionic el-ph coupling. In the weak- and intermediate-correlation regimes, we find that the on-site Coulomb interaction U acts to effectively suppress the ionic el-ph coupling at all electron and phonon momenta. In this regime, our numerical simulations are in good agreement with the results of perturbation theory to order ${U}^{2}.$ However, entering the strong-correlation regime, we find that the forward-scattering process stops decreasing and begins to substantially increase as a function of U, leading to an effective el-ph coupling which is peaked in the forward direction. Whereas at weak and intermediate Coulomb interactions, screening is the dominant correlation effect suppressing the el-ph coupling, at larger U values irreducible vertex corrections become more important and give rise to this increase. These vertex corrections depend crucially on the renormalized electronic structure of the strongly correlated system.

DOI: 10.1103/physrevb.68.220507

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arXiv:cond-mat/0306131 · Physical review. B, Condensed matter

Electron-phonon vertex in the two-dimensional one-band Hubbard model

Zhongbing Huang, Werner R. Hanke, Enrico Arrigoni, Douglas J. Scalapino

Published Dec 24, 2003• 85 citations

arXiv HTML PDF

Abstract

{U}^{2}.

However, entering the strong-correlation regime, we find that the forward-scattering process stops decreasing and begins to substantially increase as a function of U, leading to an effective el-ph coupling which is peaked in the forward direction. Whereas at weak and intermediate Coulomb interactions, screening is the dominant correlation effect suppressing the el-ph coupling, at larger U values irreducible vertex corrections become more important and give rise to this increase. These vertex corrections depend crucially on the renormalized electronic structure of the strongly correlated system.

DOI: 10.1103/physrevb.68.220507

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Renormalization of the electron-phonon interaction in presence of charge fluctuations

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We investigate the effect of strong electron correlations on the coupling of electrons to Holstein phonons in the one-band Hubbard model in the presence of charge fluctuations. Specifically, we analyze the momentum modulation of the electron-phonon vertex induced by the electronic correlations. The role of the on-site Coulomb interaction $U$ is investigated in different regions of the Brillouin zone. The results reveal the presence of a strong forward scattering peak at low temperatures and, after an initial decrease with $U$ , we find that the electron-phonon vertex starts to increase above an intermediate value of the Coulomb interaction. We show that this behavior is related to an incipient phase separation that takes place at a critical value of $U$ for fixed doping. A comparison with other approaches is also discussed.We investigate the effect of strong electron correlations on the coupling of electrons to Holstein phonons in the one-band Hubbard model in the presence of charge fluctuations. Specifically, we analyze the momentum modulation of the electron-phonon vertex induced by the electronic correlations. The role of the on-site Coulomb interaction $U$ is investigated in different regions of the Brillouin zone. The results reveal the presence of a strong forward scattering peak at low temperatures and, after an initial decrease with $U$, we find that the electron-phonon vertex starts to increase above an intermediate value of the Coulomb interaction. We show that this behavior is related to an incipient phase separation that takes place at a critical value of $U$ for fixed doping. A comparison with other approaches is also discussed.

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In cond-mat/0306131 Huang {\em et al.} reported for the first time a numerical evidence for the predominance of small phonon momenta in the electron-phonon coupling induced by electronic correlation. They report also an upturn of the electron-phonon vertex function for small momenta as function of the Hubbard repulsion $U$ for sufficient large $U$ . In this comment we compare their Quantum Monte Carlo data with analytical results based on slave-boson techniques for generic $U$ . We associate the upturn of the electron-phonon vertex function with the tendency towards a phase separation instability at large temperatures.In cond-mat/0306131 Huang {\em et al.} reported for the first time a numerical evidence for the predominance of small phonon momenta in the electron-phonon coupling induced by electronic correlation. They report also an upturn of the electron-phonon vertex function for small momenta as function of the Hubbard repulsion $U$ for sufficient large $U$. In this comment we compare their Quantum Monte Carlo data with analytical results based on slave-boson techniques for generic $U$. We associate the upturn of the electron-phonon vertex function with the tendency towards a phase separation instability at large temperatures.

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E. Cappelluti, Benedetta Cerruti, L. Pietronero

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.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.

arXiv:cond-mat/0312654Physical Review BApr 15, 200425 citations

{U}^{2}.

U

is investigated in different regions of the Brillouin zone. The results reveal the presence of a strong forward scattering peak at low temperatures and, after an initial decrease with

U

, we find that the electron-phonon vertex starts to increase above an intermediate value of the Coulomb interaction. We show that this behavior is related to an incipient phase separation that takes place at a critical value of

U

for fixed doping. A comparison with other approaches is also discussed.

{\mathit{F}}_{1}

is in the t model somewhat, in the tt\ensuremath{'} model rather strongly suppressed, especially near half-filling; the other symmetry components ${\mathrm{\ensuremath{\alpha}}}^{2}$

{\mathit{F}}_{\mathit{i}}

with i=2,...,5 increase strongly with decreasing doping and are of similar magnitude as ${\mathrm{\ensuremath{\alpha}}}^{2}$

{\mathit{F}}_{1}

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-

{\mathit{T}}_{\mathit{c}}

compounds. \textcopyright{} 1996 The American Physical Society.

U

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

U

, the electron-phonon coupling starts to increase with

U

, 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.

U

for sufficient large

U

. In this comment we compare their Quantum Monte Carlo data with analytical results based on slave-boson techniques for generic

U

. We associate the upturn of the electron-phonon vertex function with the tendency towards a phase separation instability at large temperatures.

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.