Electric polarization as a nonquantized topological response and boundary Luttinger theorem
Bibliographic record
Abstract
We develop a nonperturbative approach to the bulk polarization of crystalline electric insulators in d 1 dimensions. Formally, we define polarization via the response to background fluxes of both charge and lattice translation symmetries. In this approach, the bulk polarization is related to properties of magnetic monopoles under translation symmetries. Specifically, in 2D, the monopole is a source of 2 flux, and the polarization is determined by the crystal momentum of the 2 flux. In 3D, the polarization is determined by the projective representation of translation symmetries on Dirac monopoles. Our approach also leads to a concrete scheme to calculate polarization in 2D, which in principle can be applied even to strongly interacting systems. For open boundary conditions, the bulk polarization leads to an altered boundary Luttinger theorem (constraining the Fermi surface of surface states) and also to modified Lieb-Schultz-Mattis theorems on the boundary, which we derive.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".