Spectral function tour of electron-phonon coupling outside the Migdal limit
Bibliographic record
Abstract
We simulate spectral functions for electron-phonon coupling in a filled band system---far from the asymptotic limit often assumed where the phonon energy is very small compared to the Fermi energy in a parabolic band and the Migdal theorem predicting $(1+\ensuremath{\lambda})$ quasiparticle renormalizations is valid. These spectral functions are examined over a wide range of parameter space through techniques often used in angle-resolved photoemission spectroscopy. Analyzing over 1200 simulations we consider variations of the microscopic coupling strength, phonon energy, and dimensionality for two models: a momentum-independent Holstein model, and momentum-dependent coupling to a breathing mode phonon. In this limit we find that any ``effective coupling'' ${\ensuremath{\lambda}}_{\text{eff}}$ inferred from the quasiparticle renormalizations differs from the microscopic coupling characterizing these Hamiltonians $\ensuremath{\lambda}$, and could drastically either overestimate or underestimate it, depending on the particular parameters and model. In contrast, we show that perturbation theory retains good predictive power for low coupling and small momenta, and that the momentum dependence of the self-energy can be revealed via the relationship between velocity renormalization and quasiparticle strength. Additionally, we find that (although not strictly valid) it is often possible to infer the self-energy and bare electronic structure through a self-consistent Kramers-Kronig bare-band fitting; and also that through line shape alone, when Lorentzian, it is possible to reliably extract the shape of the imaginary part of a momentum-dependent self-energy without reference to the bare band.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".