Abstract
Determining the range of validity of Migdal’s approximation for electron-phonon (e-ph) coupled systems is a long-standing problem. Many attempts to answer this question employ the Holstein Hamiltonian, where the electron density couples linearly to local lattice displacements. When these displacements are large, however, nonlinear corrections to the interaction must also be included, which can significantly alter the physical picture obtained from this model. Using determinant quantum Monte Carlo and the self-consistent Migdal approximation, we compared superconducting and charge-density-wave correlations in the Holstein model with and without second-order nonlinear interactions. We find a disagreement between the two cases, even for relatively small values of the e-ph coupling strength, and, importantly, that this can occur in the same parameter regions where Migdal’s approximation holds. Our results demonstrate that questions regarding the validity of Migdal’s approximation go hand in hand with questions of the validity of a linear e-ph interaction.
| Original language | English |
|---|---|
| Article number | 145 |
| Journal | Communications Physics |
| Volume | 3 |
| Issue number | 1 |
| DOIs | |
| State | Published - Dec 1 2020 |
Funding
We thank M. Berciu and D.J. Scalapino for providing early feedback on the manuscript. We also thank B. Cohen-Stead. and R.T. Scalettar for valuable discussions regarding the length scales discussed in this work. This work is supported by the Scientific Discovery through Advanced Computing (SciDAC) program funded by the U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research and Basic Energy Sciences, Division of Materials Sciences and Engineering. J.C. recognizes the support of the DOE Computational Science Graduate Fellowship (CSGF) under Grant DE-FG02-97ER25308. This research also used resources of the Oak Ridge Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC05-00OR22725.