Efficient Migdal-Eliashberg calculations with Intermediate Representation basis using the EPW code

Recent attempts have been made to reduce the number of frequency points for the Matsubara Green’s functions in finite-temperature many-body calculations in order to reduce the computational cost. A method based on the intermediate Representation (IR) basis [1] has proven successful for computing the transition temperature within the Migdal-Eliashberg approach for several superconductors, such as Nb and H₃S [2,3]. However, the calculations performed in these studies have been limited to a k-averaged electron-phonon interaction kernel. We have taken a step forward and implemented the IR basis method in the EPW code to solve the anisotropic full-bandwidth Migdal-Eliashberg equations [4]. This enables accurate and efficient calculations of the superconducting gap and critical temperature on ultra-dense electron k and phonon q grids. In this talk, we will discuss the implementation and show results of some representative systems obtained using the EPW code with the IR basis.

[1] H. Shinaoka et al., Phys. Rev. B 96, 035147 (2017).

[2] T. Wang et al., Phys. Rev. B 102, 134503 (2020).

[3] T. Wang et al., Phys. Rev. B 104, 064510 (2021).

[4] S. Poncé et al., Comput. Phys. Commun. 209 116 (2016).