Emergent anomalies and generalized Luttinger theorems in metals and semimetals
Bibliographic record
Abstract
Whether a given material is a metal or an insulator is determined by a single parameter, the number of electrons per unit cell per spin, that is, by the filling number. When the latter is integer, the material is an insulator or a compensated semimetal. When it is fractional, the material is a metal with a Fermi surface, enclosing a volume in momentum space, determined by the fractional part of the filling -- a statement known as Luttinger's theorem. Topological semimetals provide a realization of the metallic phase, distinct from ordinary metals, as they exist at integer fillings, which normally correspond to insulators. Here, the authors develop a framework that unifies Luttinger's theorem for ordinary metals and analogous exact statements for topological semimetals. They use the language of quantum anomalies of the emergent low-energy charge conservation symmetry at each point on the Fermi surface. This framework allows one to connect topological responses in all nodal semimetals to their low-energy properties, such as the distance between the point nodes in momentum space or the area, enclosed by the nodal line.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 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) | 0.001 | 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".