"Breakdown of the Migdal-Eliashberg theory: A determinant quantum Monte Carlo study"

I. Esterlis: B. Nosarzewski, E. W. Huang, B. Moritz, T. P. Devereaux, D. J. Scalapino, and S. A. Kivelson; Physical Review B, 04/02/18.

Additional Authors: B. Nosarzewski, E. W. Huang, B. Moritz, T. P. Devereaux, D. J. Scalapino, and S. A. Kivelson

Abstract:

The superconducting (SC) and charge-density-wave (CDW) susceptibilities of the two-dimensional Holstein model are computed using determinant quantum Monte Carlo, and compared with results computed using the Migdal-Eliashberg (ME) approach. We access temperatures as low as 25 times less than the Fermi energy, EF, which are still above the SC transition. We find that the SC susceptibility at low T agrees quantitatively with the ME theory up to a dimensionless electron-phonon coupling λ0≈0.4 but deviates dramatically for larger λ0. We find that for large λ0 and small phonon frequency ω0EF CDW ordering is favored and the preferred CDW ordering vector is uncorrelated with any obvious feature of the Fermi surface.