Relevance of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Cu</mml:mi><mml:mo>–</mml:mo><mml:mn>3</mml:mn><mml:mi>d</mml:mi></mml:mrow></mml:math> multiplet structure in models of high-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>T</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math> cuprates
Bibliographic record
Abstract
We revisit the problem of the spectra of two holes in a ${\mathrm{CuO}}_{2}$ layer, modeled as a $\mathrm{Cu}\text{\ensuremath{-}}3{d}^{8}$ impurity with full multiplet structure coupled to a full O-$2p$ band as an approximation to the local electronic structure of a hole-doped cuprate. Unlike previous studies that treated the O band as a featureless bath, we describe it with a realistic tight-binding model. While our results are in qualitative agreement with previous work, we find considerable quantitative changes when using the proper O-$2p$ band structure. We also find that (i) the ligand O-$2p$ orbitals play an essential role, within this impurity model; (ii) the three-orbital Emery model provides an accurate description for the subspace with $^{1}A_{1}$ symmetry, which includes the ground state in the relevant region of the phase diagram; (iii) this ground state has only $\ensuremath{\sim}50%$ overlap with a Zhang-Rice singlet; (iv) there are other low-energy states, in subspaces with different symmetries, that are absent from the three-orbital Emery model and its one-band descendants. These states play an important role in describing the elementary excitations of doped cuprates.
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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 | 0.003 | 0.003 |
| Meta-epidemiology (narrow) | 0.002 | 0.004 |
| Meta-epidemiology (broad) | 0.002 | 0.006 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.001 | 0.005 |
| Open science | 0.005 | 0.004 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.032 | 0.004 |
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; both teacher heads agree on what is shown here.
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".