Two-particle self-consistent approximation, pseudogap and\n superconductivity in the attractive Hubbard model
Bibliographic record
Abstract
In this thesis, I present a non-perturbative approach to the single-band\nattractive Hubard model which is an extension of previous work by Vilk and\nTremblay on the repulsive model. Exact results are derived in the general\ncontext of functional derivative approaches to many-body theories. The first\nstep of the approximation is based on a local field type ansatz. All physical\nquantities can be expressed as a function of double-occupancy (in addition to\ntemperature and filling). Double-occupancy is determined without adjustable\nparameter by imposing the Pauli principle and a crucial sum-rule, making the\nfirst step of the approximation Two-Particle Self-Consistent. The final\nexpression for the self-energy is obtained by calculating the low-frequency\npart of the exact expression with the two-particle correlation, Green function\nand renormalized vertex obtained in the first step of the approximation. The\nMermin-Wagner theorem in two dimensions is automatically satisfied. Application\nof this non-perturbative many-body approach to the intermediate coupling regime\nshows quantitative agreement with quantum Monte Carlo calculations. Both\napproaches predict the existence of a pseudogap in the single-particle spectral\nweight. I present some physical properties, such as correlation lengths,\nsuperfluid density, and characteristic pair fluctuation energy, to highlight\nthe origin of the pseudogap in the weak to intermediate coupling regime. These\nresults suggest that two-dimensional systems that are described by a symmetry\ngroup larger than SO(2) could have a larger region of pseudogap behavior.\nHigh-temperature superconductors may belong to that category of systems.\n
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 source (direct Gemma or distilled Codex), 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".