Comment on "Towards exact solutions for the superconducting $T_c$ induced by electron-phonon interaction"

Abstract

In a series of recent articles, Liu, Yang, Pan, et al. 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.

comment on Phys. Rev. B 103, 094501 (2021), arXiv:1911.05528 ; 2 pages, 0 figures

References in corpus (4)

• Nonperturbative Dyson-Schwinger equation approach to strongly interacting Dirac fermion systems
• A non-perturbative study of the interplay between electron-phonon interaction and Coulomb interaction in undoped graphene
• Fermion dispersion renormalization in a two-dimensional semi-Dirac semimetal
• Theoretical study of phonon-mediated superconductivity beyond Migdal-Eliashberg approximation and Coulomb pseudopotential