Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0401089 · Physical Review B

Renormalization of the electron-phonon coupling in the one-band Hubbard model

Erik Koch, R. Zeyher

Published Sep 21, 2004• 29 citations
arXivHTMLPDF

Abstract

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 $U$ 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.

DOI
10.1103/physrevb.70.094510

Related papers

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

R. Citro, S. Cojocaru, M. Marinaro

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.

Physical Review B•Sep 12, 2005•8 citations

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

Zhongbing Huang, Werner R. Hanke, Enrico Arrigoni +1 more

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.

arXiv:cond-mat/0306131•Physical review. B, Condensed matter•Dec 24, 2003•85 citations

Renormalization of the electron-phonon interaction by strong electronic correlations in high- Tc superconductors

R. Zeyher, Miodrag L. Kulić

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}$${\mathit{F}}_{1}$ is in the t model somewhat, in the tt\ensuremath{'} model rather strongly suppressed, especially near half-filling; the other symmetry components ${\mathrm{\ensuremath{\alpha}}}^{2}$${\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.

Physical review. B, Condensed matter•Feb 1, 1996•147 citations

Comment on ``Electron-phonon Vertex in the Two-dimensional One-band Hubbard Model''

Benedetta Cerruti, E. Cappelluti, L. Pietronero

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.

arXiv:cond-mat/0307190•Jul 9, 2003•0 citations

Low quasiparticle coherence temperature in the one-band Hubbard model: A slave-boson approach

Alejandro Mezio, Ross H. McKenzie

We use the Kotliar-Ruckenstein slave-boson formalism to study the temperature dependence of paramagnetic phases of the one-band Hubbard model for a variety of band structures. We calculate the Fermi liquid quasiparticle spectral weight $Z$ and identify the temperature at which it decreases significantly to a crossover to a bad metal region. Near the Mott metal-insulator transition, this coherence temperature ${T}_{\mathrm{coh}}$ is much lower than the Fermi temperature of the uncorrelated Fermi gas, as is observed in a broad range of strongly correlated electron materials. After a proper rescaling of temperature and interaction, we find a universal behavior that is independent of the band structure of the system. We obtain the temperature-interaction phase diagram as function of doping, and we compare the temperature dependence of the double occupancy, entropy, and charge compressibility with previous results obtained with dynamical mean-field theory. We analyze the stability of the method by calculating the charge compressibility.

arXiv:1702.02796•Physical review. B./Physical review. B•Jul 13, 2017•12 citations

Effects of electron-phonon coupling near and within the insulating Mott phase

C. A. Perroni, V. Cataudella, G. De Filippis +1 more

The role of the electron-phonon interaction in the Holstein-Hubbard model is investigated in the metallic phase close to the Mott transition and in the insulating Mott phase. The model is studied by means of a variational slave boson technique. At half-filling, mean-field static quantities are in good agreement with the results obtained by numerical techniques. By taking into account Gaussian fluctuations, an analytic expression of the spectral density is derived in the Mott insulating phase showing that an increase of the electron-phonon coupling leads to a sensitive reduction of the Mott gap through a reduced effective repulsion. The relation of the results with recent experimental observations in strongly correlated systems is discussed.

arXiv:cond-mat/0412243•Physical Review B•Mar 31, 2005•18 citations
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∼tkT\ensuremath{\sim}tkT\ensuremath∼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.
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 UUU 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 UUU, 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 UUU for fixed doping. A comparison with other approaches is also discussed.
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 U2.{U}^{2}.U2. 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.
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.
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 UUU for sufficient large UUU. In this comment we compare their Quantum Monte Carlo data with analytical results based on slave-boson techniques for generic UUU. We associate the upturn of the electron-phonon vertex function with the tendency towards a phase separation instability at large temperatures.
We use the Kotliar-Ruckenstein slave-boson formalism to study the temperature dependence of paramagnetic phases of the one-band Hubbard model for a variety of band structures. We calculate the Fermi liquid quasiparticle spectral weight ZZZ and identify the temperature at which it decreases significantly to a crossover to a bad metal region. Near the Mott metal-insulator transition, this coherence temperature Tcoh{T}_{\mathrm{coh}}Tcoh​ is much lower than the Fermi temperature of the uncorrelated Fermi gas, as is observed in a broad range of strongly correlated electron materials. After a proper rescaling of temperature and interaction, we find a universal behavior that is independent of the band structure of the system. We obtain the temperature-interaction phase diagram as function of doping, and we compare the temperature dependence of the double occupancy, entropy, and charge compressibility with previous results obtained with dynamical mean-field theory. We analyze the stability of the method by calculating the charge compressibility.
The role of the electron-phonon interaction in the Holstein-Hubbard model is investigated in the metallic phase close to the Mott transition and in the insulating Mott phase. The model is studied by means of a variational slave boson technique. At half-filling, mean-field static quantities are in good agreement with the results obtained by numerical techniques. By taking into account Gaussian fluctuations, an analytic expression of the spectral density is derived in the Mott insulating phase showing that an increase of the electron-phonon coupling leads to a sensitive reduction of the Mott gap through a reduced effective repulsion. The relation of the results with recent experimental observations in strongly correlated systems is discussed.