We derive sum rules for the phonon self-energy and the electron-phonon contribution to the electron self-energy of the Holstein-Hubbard model in the limit of large Coulomb interaction $U$ . Their relevance for finite $U$ is investigated using exact diagonalization and dynamical mean-field theory. Based on these sum rules, we study the importance of vertex corrections to the electron-phonon interaction in a diagrammatic approach. We show that they are crucial for a sum rule for the electron self-energy in the undoped system while a sum rule related to the phonon self-energy of doped systems is satisfied even if vertex corrections are neglected. We provide explicit results for the vertex function of a two-site model.We derive sum rules for the phonon self-energy and the electron-phonon contribution to the electron self-energy of the Holstein-Hubbard model in the limit of large Coulomb interaction $U$. Their relevance for finite $U$ is investigated using exact diagonalization and dynamical mean-field theory. Based on these sum rules, we study the importance of vertex corrections to the electron-phonon interaction in a diagrammatic approach. We show that they are crucial for a sum rule for the electron self-energy in the undoped system while a sum rule related to the phonon self-energy of doped systems is satisfied even if vertex corrections are neglected. We provide explicit results for the vertex function of a two-site model.

arXiv:cond-mat/0607612Physical Review BJan 17, 200712 citations

Effect of Electron Correlation on Phonon Spectra in Cuprates

Kenji Tsutsui, Takami Tohyama, Sadamichi Maekawa

Journal of Low Temperature PhysicsApr 7, 20035 citations

Electron-phonon coupling in the self-consistent Born approximation of the t−J model

O. Gunnarsson, O. Rösch

We study an undoped $t\text{\ensuremath{-}}J$ model with electron-phonon interaction using the self-consistent Born approximation (SCBA). By neglecting vertex corrections, the SCBA solves a boson-holon model, where a holon couples to phonons and magnons. Comparison with exact diagonalization results for the $t\text{\ensuremath{-}}J$ model suggests that the SCBA describes the electron-phonon interaction fairly accurately over a substantial range of $J∕t$ values. Exact diagonalization of the boson-holon model shows that the deviations are mainly due to the neglect of vertex corrections for small $J∕t$ and due to the replacement of the $t\text{\ensuremath{-}}J$ model by the boson-holon model for large $J∕t$ . For typical values of $J∕t$ , the electron-phonon part ${\ensuremath{\Sigma}}_{\mathrm{ep}}$ of the electron self-energy has comparable contributions from the second-order diagram in the electron-phonon interaction and a phonon-induced change of magnon diagrams. A very simple approximation to ${\ensuremath{\Sigma}}_{\mathrm{ep}}$ gives a rather accurate effective mass. Using this approximation, we study the factors influencing the electron-phonon interaction. Typically, we find that the magnons nominally have a stronger coupling to the holon than the phonons. The phonons, nevertheless, drive the formation of small polarons (self-localization) due to important differences between the character of the phonon and magnon couplings.We study an undoped $t\text{\ensuremath{-}}J$ model with electron-phonon interaction using the self-consistent Born approximation (SCBA). By neglecting vertex corrections, the SCBA solves a boson-holon model, where a holon couples to phonons and magnons. Comparison with exact diagonalization results for the $t\text{\ensuremath{-}}J$ model suggests that the SCBA describes the electron-phonon interaction fairly accurately over a substantial range of $J∕t$ values. Exact diagonalization of the boson-holon model shows that the deviations are mainly due to the neglect of vertex corrections for small $J∕t$ and due to the replacement of the $t\text{\ensuremath{-}}J$ model by the boson-holon model for large $J∕t$. For typical values of $J∕t$, the electron-phonon part ${\ensuremath{\Sigma}}_{\mathrm{ep}}$ of the electron self-energy has comparable contributions from the second-order diagram in the electron-phonon interaction and a phonon-induced change of magnon diagrams. A very simple approximation to ${\ensuremath{\Sigma}}_{\mathrm{ep}}$ gives a rather accurate effective mass. Using this approximation, we study the factors influencing the electron-phonon interaction. Typically, we find that the magnons nominally have a stronger coupling to the holon than the phonons. The phonons, nevertheless, drive the formation of small polarons (self-localization) due to important differences between the character of the phonon and magnon couplings.

arXiv:cond-mat/0602327Physical Review BMay 23, 200624 citations

Temperature Dependence of the Angle Resolved Photoemission Spectra in the Undoped Cuprates: Self-Consistent Approach to the t−J Holstein Model

V. Cataudella, G. De Filippis, Andrei S. Mishchenko +1 more

We develop a novel self-consistent approach for studying the angle resolved photoemission spectra (ARPES) of a hole in the t-J Holstein model giving perfect agreement with numerically exact diagrammatic Monte Carlo (DMC) data at zero temperature for all regimes of electron-phonon coupling. Generalizing the approach to finite temperatures, we find that the anomalous temperature dependence of the ARPES in undoped cuprates is explained by cooperative interplay of coupling of the hole to magnetic fluctuations and strong electron-phonon interaction.We develop a novel self-consistent approach for studying the angle resolved photoemission spectra (ARPES) of a hole in the t-J Holstein model giving perfect agreement with numerically exact diagrammatic Monte Carlo (DMC) data at zero temperature for all regimes of electron-phonon coupling. Generalizing the approach to finite temperatures, we find that the anomalous temperature dependence of the ARPES in undoped cuprates is explained by cooperative interplay of coupling of the hole to magnetic fluctuations and strong electron-phonon interaction.

arXiv:0707.3076Physical Review LettersNov 30, 200744 citations

Renormalization of the electron–phonon interaction in the Hubbard model

R. Citro, S. Cojocaru, M. Marinaro

Physica B Condensed MatterFeb 18, 20050 citations

We derive sum rules for the phonon self-energy and the electron-phonon contribution to the electron self-energy of the Holstein-Hubbard model in the limit of large Coulomb interaction

U

. Their relevance for finite

U

is investigated using exact diagonalization and dynamical mean-field theory. Based on these sum rules, we study the importance of vertex corrections to the electron-phonon interaction in a diagrammatic approach. We show that they are crucial for a sum rule for the electron self-energy in the undoped system while a sum rule related to the phonon self-energy of doped systems is satisfied even if vertex corrections are neglected. We provide explicit results for the vertex function of a two-site model.

J∕t

values. Exact diagonalization of the boson-holon model shows that the deviations are mainly due to the neglect of vertex corrections for small

J∕t

and due to the replacement of the $t\text{\ensuremath{-}}J$ model by the boson-holon model for large

J∕t

. For typical values of

J∕t

, the electron-phonon part ${\ensuremath{\Sigma}}_{\mathrm{ep}}$ of the electron self-energy has comparable contributions from the second-order diagram in the electron-phonon interaction and a phonon-induced change of magnon diagrams. A very simple approximation to ${\ensuremath{\Sigma}}_{\mathrm{ep}}$ gives a rather accurate effective mass. Using this approximation, we study the factors influencing the electron-phonon interaction. Typically, we find that the magnons nominally have a stronger coupling to the holon than the phonons. The phonons, nevertheless, drive the formation of small polarons (self-localization) due to important differences between the character of the phonon and magnon couplings.