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

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, 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 ≈ 0.4 but deviates dramatically for larger λ 0. We find that for large λ 0 and small phonon frequency ω 0 << E F CDW ordering is favored and the preferred CDW ordering vector is uncorrelated with any obvious feature of the Fermi surface.

Authors:
 [1];  [2];  [2];  [3];  [4];  [5];  [6]
  1. Stanford Univ., CA (United States). Dept. of Physics
  2. Stanford Univ., CA (United States). Dept. of Physics; SLAC National Accelerator Lab., Menlo Park, CA (United States). Stanford Institute for Materials and Energy Science (SIMES)
  3. SLAC National Accelerator Lab., Menlo Park, CA (United States). Stanford Institute for Materials and Energy Science (SIMES)
  4. SLAC National Accelerator Lab., Menlo Park, CA (United States). Stanford Institute for Materials and Energy Science (SIMES); Stanford Univ., CA (United States). Geballe Lab. for Advanced Materials
  5. Univ. of California, Santa Barbara, CA (United States). Dept. of Physics
  6. Stanford Univ., CA (United States). Dept. of Physics; Stanford Univ., CA (United States). Geballe Lab. for Advanced Materials
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); National Science Foundation (NSF); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1436079
Alternate Identifier(s):
OSTI ID: 1430775
Grant/Contract Number:  
AC02-76SF00515; DMR-1608055; PHY11-25915
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 97; Journal Issue: 14; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Esterlis, I., Nosarzewski, B., Huang, E. W., Moritz, B., Devereaux, T. P., Scalapino, D. J., and Kivelson, S. A. Breakdown of the Migdal-Eliashberg theory: A determinant quantum Monte Carlo study. United States: N. p., 2018. Web. doi:10.1103/physrevb.97.140501.
Esterlis, I., Nosarzewski, B., Huang, E. W., Moritz, B., Devereaux, T. P., Scalapino, D. J., & Kivelson, S. A. Breakdown of the Migdal-Eliashberg theory: A determinant quantum Monte Carlo study. United States. doi:10.1103/physrevb.97.140501.
Esterlis, I., Nosarzewski, B., Huang, E. W., Moritz, B., Devereaux, T. P., Scalapino, D. J., and Kivelson, S. A. Mon . "Breakdown of the Migdal-Eliashberg theory: A determinant quantum Monte Carlo study". United States. doi:10.1103/physrevb.97.140501. https://www.osti.gov/servlets/purl/1436079.
@article{osti_1436079,
title = {Breakdown of the Migdal-Eliashberg theory: A determinant quantum Monte Carlo study},
author = {Esterlis, I. and Nosarzewski, B. and Huang, E. W. and Moritz, B. and Devereaux, T. P. and Scalapino, D. J. and Kivelson, S. A.},
abstractNote = {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 ω0 << EF CDW ordering is favored and the preferred CDW ordering vector is uncorrelated with any obvious feature of the Fermi surface.},
doi = {10.1103/physrevb.97.140501},
journal = {Physical Review B},
number = 14,
volume = 97,
place = {United States},
year = {2018},
month = {4}
}

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