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:2404.02918 · Physical review. B./Physical review. B

Comment on “Towards exact solutions for the superconducting T c induced by electron-phonon interaction”

Grgur Palle

Published Jul 22, 2024• 1 citation
arXivHTMLPDF

Abstract

In a series of recent papers starting with , Liu, Yang, Pan claim to have determined the exact dressed electron-boson vertex for a number of very general interacting many-body problems by inverting certain Ward-Takahashi identities. Here, we point out that their Ward-Takahashi identities are missing terms which make the inversion of the identities impossible. One therefore cannot formulate exact self-contained integral equations for the dressed electron propagator. In addition, the proposed vertex expressions do not reproduce well-established results for the leading perturbative corrections. Published by the American Physical Society 2024

DOI
10.1103/physrevb.110.026501

Related papers

Ward identity preserving approach for investigation of phonon spectrum with self-energy and vertex corrections

Sudhakar Pandey

We propose an approach for investigating the many-body effects on the phonon spectrum in an electron-phonon coupled system by taking into account the electron self-energy and vertex corrections which respect the Ward identity representing the conservation of electronic charge. Our approach provides a systematic diagrammatic expansion of the phonon self-energy ${\mathrm{\ensuremath{\Pi}}}_{\mathbf{q}}(\ensuremath{\omega})$ in powers of the electron-phonon scattering strength squared $({g}^{2})$. In this approach the many-body corrections to the phonon spectrum vanish identically for the $\mathbf{q}=0$ mode due to an exact cancellation between the contributions arising from electron self-energy and vertex corrections. This cancellation holds irrespective of the microscopic details of the system such as dimensionality, adiabaticity, strength of electron-phonon scattering, etc. Our results demonstrate that the contributions of electron self-energy and vertex corrections are not only comparable but they also tend to cancel each other so that the phonon spectrum remains nearly unaffected due to many-body effects in the regime of long-wavelength excitations ($\mathbf{q}\ensuremath{\rightarrow}0$). Our results provide another constraint for the applicability of the Migdal theorem.

arXiv:2308.14379•Physical review. B./Physical review. B•Aug 23, 2024•0 citations

Role of the ward identity and relevance of the G0W0 approximation in normal and superconducting states

Yasutami Takada

On the basis of the self-consistent calculation scheme for the electron self-energy Σ with the use of the three-point vertex function Γ always satisfying the Ward identity, we find that the obtained quasi-particle dispersion in the normal state in gapped systems, such as semiconductors, insulators, and molecules, is well reproduced by that in the one-shot GW (or G0W0) approximation. In calculating the superconducting transition temperature Tc, we also find a similar situation; the result for Tc in the gauge-invariant self-consistent framework including the effect of Γ satisfying the Ward identity is different from that in the conventional Eliashberg theory (which amounts to the GW approximation for superconductivity) but is close to that in the G0W0 approximation. Those facts indicate that the G0W0 approximation actually takes proper account of both vertex and high-order self-energy corrections in a mutually cancelling manner and thus we can understand that the G0W0 approximation is better than the fully self-consistent GW one in obtaining some of physical quantities.

arXiv:1601.02364•Molecular Physics•Jan 8, 2016•5 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.

arXiv:cond-mat/0602327•Physical Review B•May 23, 2006•24 citations

Nonperturbative Dyson-Schwinger equation approach to strongly interacting Dirac fermion systems

Xiao‐Yin Pan, Zhao-Kun Yang, Xin Li +1 more

Studying the strong correlation effects in interacting Dirac fermion systems is one of the most challenging problems in modern condensed matter physics. The long-range Coulomb interaction and the fermion-phonon interaction can lead to a variety of intriguing properties. In the strong-coupling regime, weak-coupling perturbation theory breaks down. The validity of $1/N$ expansion with $N$ being the fermion flavor is also in doubt since $N$ equals to 2 or 4 in realistic systems. Here, we investigate the interaction between $(1+2)$- and $(1+3)$-dimensional massless Dirac fermions and a generic scalar boson, and develop an efficient nonperturbative approach to access the strong-coupling regime. We first derive a number of self-consistently coupled Ward-Takahashi identities based on a careful symmetry analysis and then use these identities to show that the full fermion-boson vertex function is solely determined by the full fermion propagator. Making use of this result, we rigorously prove that the full fermion propagator satisfies an exact and self-closed Dyson-Schwinger integral equation, which can be solved by employing numerical methods. A major advantage of our nonperturbative approach is that there is no need to employ any small expansion parameter. Our approach provides a unified theoretical framework for studying strong Coulomb and fermion-phonon interactions. It may also be used to approximately handle the Yukawa coupling between fermions and order-parameter fluctuations around continuous quantum critical points. Our approach is applied to treat the Coulomb interaction in undoped graphene. We find that the renormalized fermion velocity exhibits a logarithmic momentum dependence but is nearly energy independent, and that no excitonic gap is generated by the Coulomb interaction. These theoretical results are consistent with experiments in graphene.

arXiv:2003.10371•Physical review. B./Physical review. B•Aug 23, 2021•10 citations

Comment on “Integrable Chain of Electrons Interacting With Phonons,” By M. E. Zhuravlev, V. A. Ivanov, and V. V. Achkasov, JETP Lett. 63, 94 (1996)

F. Marsiglio

We note that the exactly solvable electron-phonon Hamiltonian presented in that paper can be solved by a more direct route via the Lang-Firsov transformation.

Journal of Experimental and Theoretical Physics Letters•Dec 1, 1996•0 citations

Comment on “Electron Spectral Function and Algebraic Spin Liquid for the Normal State of Underdoped High Tc Superconductors”

Dmitri V. Khveshchenko

Comment on the Letter by W. Rantner and X-G. Wen, Phys. Rev. Lett. v.86, p.3871 (2001).

arXiv:cond-mat/0306079•Physical Review Letters•May 13, 2003•5 citations
In a series of recent papers starting with , Liu, Yang, Pan claim to have determined the exact dressed electron-boson vertex for a number of very general interacting many-body problems by inverting certain Ward-Takahashi identities. Here, we point out that their Ward-Takahashi identities are missing terms which make the inversion of the identities impossible. One therefore cannot formulate exact self-contained integral equations for the dressed electron propagator. In addition, the proposed vertex expressions do not reproduce well-established results for the leading perturbative corrections. Published by the American Physical Society 2024
We propose an approach for investigating the many-body effects on the phonon spectrum in an electron-phonon coupled system by taking into account the electron self-energy and vertex corrections which respect the Ward identity representing the conservation of electronic charge. Our approach provides a systematic diagrammatic expansion of the phonon self-energy ${\mathrm{\ensuremath{\Pi}}}_{\mathbf{q}}(\ensuremath{\omega})$ in powers of the electron-phonon scattering strength squared (g2)({g}^{2})(g2). In this approach the many-body corrections to the phonon spectrum vanish identically for the q=0\mathbf{q}=0q=0 mode due to an exact cancellation between the contributions arising from electron self-energy and vertex corrections. This cancellation holds irrespective of the microscopic details of the system such as dimensionality, adiabaticity, strength of electron-phonon scattering, etc. Our results demonstrate that the contributions of electron self-energy and vertex corrections are not only comparable but they also tend to cancel each other so that the phonon spectrum remains nearly unaffected due to many-body effects in the regime of long-wavelength excitations ($\mathbf{q}\ensuremath{\rightarrow}0$). Our results provide another constraint for the applicability of the Migdal theorem.
On the basis of the self-consistent calculation scheme for the electron self-energy Σ with the use of the three-point vertex function Γ always satisfying the Ward identity, we find that the obtained quasi-particle dispersion in the normal state in gapped systems, such as semiconductors, insulators, and molecules, is well reproduced by that in the one-shot GW (or G0W0) approximation. In calculating the superconducting transition temperature Tc, we also find a similar situation; the result for Tc in the gauge-invariant self-consistent framework including the effect of Γ satisfying the Ward identity is different from that in the conventional Eliashberg theory (which amounts to the GW approximation for superconductivity) but is close to that in the G0W0 approximation. Those facts indicate that the G0W0 approximation actually takes proper account of both vertex and high-order self-energy corrections in a mutually cancelling manner and thus we can understand that the G0W0 approximation is better than the fully self-consistent GW one in obtaining some of physical quantities.
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∕tJ∕tJ∕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∕tJ∕tJ∕t and due to the replacement of the $t\text{\ensuremath{-}}J$ model by the boson-holon model for large J∕tJ∕tJ∕t. For typical values of J∕tJ∕tJ∕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.
Studying the strong correlation effects in interacting Dirac fermion systems is one of the most challenging problems in modern condensed matter physics. The long-range Coulomb interaction and the fermion-phonon interaction can lead to a variety of intriguing properties. In the strong-coupling regime, weak-coupling perturbation theory breaks down. The validity of 1/N1/N1/N expansion with NNN being the fermion flavor is also in doubt since NNN equals to 2 or 4 in realistic systems. Here, we investigate the interaction between (1+2)(1+2)(1+2)- and (1+3)(1+3)(1+3)-dimensional massless Dirac fermions and a generic scalar boson, and develop an efficient nonperturbative approach to access the strong-coupling regime. We first derive a number of self-consistently coupled Ward-Takahashi identities based on a careful symmetry analysis and then use these identities to show that the full fermion-boson vertex function is solely determined by the full fermion propagator. Making use of this result, we rigorously prove that the full fermion propagator satisfies an exact and self-closed Dyson-Schwinger integral equation, which can be solved by employing numerical methods. A major advantage of our nonperturbative approach is that there is no need to employ any small expansion parameter. Our approach provides a unified theoretical framework for studying strong Coulomb and fermion-phonon interactions. It may also be used to approximately handle the Yukawa coupling between fermions and order-parameter fluctuations around continuous quantum critical points. Our approach is applied to treat the Coulomb interaction in undoped graphene. We find that the renormalized fermion velocity exhibits a logarithmic momentum dependence but is nearly energy independent, and that no excitonic gap is generated by the Coulomb interaction. These theoretical results are consistent with experiments in graphene.