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arXiv · 1711.01493

Breakdown of Migdal-Eliashberg theory; a determinant quantum Monte Carlo study

Ilya Esterlis·Benjamin Nosarzewski·Edwin W. Huang·Brian Moritz·Thomas P. Devereaux·Douglas J. Scalapino·Steven A. Kivelson
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Abstract

The superconducting (SC) and charge-density-wave (CDW) susceptibilities of the two dimensional Holstein model are computed using determinant quantum Monte Carlo (DQMC), and compared with results computed using the Migdal-Eliashberg (ME) approach. We access temperatures as low as 25 times less than the Fermi energy, $E_F$, 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 $λ_0 \approx 0.4$ but deviates dramatically for larger $λ_0$. We find that for large $λ_0$ and small phonon frequency $ω_0 \ll E_F$ CDW ordering is favored and the preferred CDW ordering vector is uncorrelated with any obvious feature of the Fermi surface.

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Ilya Esterlis, Benjamin Nosarzewski, Edwin W. Huang, Brian Moritz, Thomas P. Devereaux, Douglas J. Scalapino, Steven A. Kivelson. 2018-02-20. Breakdown of Migdal-Eliashberg theory; a determinant quantum Monte Carlo study. https://doi.org/10.1103/physrevb.97.140501

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