Renormalized phonon spectrum in the Su–Schrieffer–Heeger model
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Bibliographic record
Abstract
Abstract Motivated to understand phonon spectrum renormalization in the ground state of the half-filled Su–Schrieffer–Heeger model, we use the Born–Oppenheimer approximation together with the harmonic approximation to evaluate semi-analytically the all-to-all real-space ionic force constants generated through both linear and quadratic electron-phonon coupling. We then compute the renormalized phonon spectrum and the corresponding lattice zero-point energy (ZPE) as a function of the lattice dimerization. Crucially, the latter is included in the system’s total energy, and thus has a direct effect on the equilibrium dimerization. We find that inclusion of a small quadratic coupling leads to very significant changes in the predicted equilibrium dimerization, calling into question the use of the linear approximation for this model. We also argue that inclusion of the ZPE is key for systems with comparable lattice and electronic energies, and/or for finite size chains. Our method can be straightforwardly generalized to study similar problems in higher dimensions.
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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 | 0.001 | 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 it