Bibliographic record
Abstract
We analyze the internal symmetries and their anomalies in the Kitaev spin-S models.Importantly, these models have a lattice version of a Z2 1-form symmetry, denoted by2 .There is also an ordinary 0-formare π spin rotations around two orthogonal axes, and Z T 2 is the time reversal symmetry.The anomalies associated with the full2 symmetry are classified by Z 17 2 .We find that for S ∈ Z the model is anomalyfree, while for S ∈ Z + 1 2 there is an anomaly purely associated with the 1-form symmetry, but there is no anomaly purely associated with the ordinary symmetry or mixed anomaly between the 0-form and 1-form symmetries.The consequences of these anomalies apply to not only the Kitaev spin-S models, but also any of their perturbed versions, assuming that the perturbations are local and respect the symmetries.If these local perturbations are weak, these consequences apply even if the perturbations break the 1-form symmetry.A notable consequence is that there must be a deconfined fermionic excitation carrying no fractional quantum number under the Z (x) 2 × Z (y) 2 × Z T 2 symmetry if S ∈ Z + 1 2 .Contents I. Introduction 1 II.Kitaev spin-S model and its symmetries 2 III.1-form symmetry and its anomaly 2 IV.Full internal symmetry anomaly for S = 1/2 3 V.Even-odd effect 4 VI.Consequences of the anomaly 5 VII.Discussion 5 A. General discussion of the lattice version of a Z n 1-form symmetry in two spatial dimensions 6 1.General algebraic relations 6 2. Statistical phase factor of the end points 7 3. Gauging the Z n 1-form symmetry 8 a. Gauging the Z [1] 2 symmetry in the Kitaev spin-S model 8 b.Gauging a Z n 1-form symmetry 9 4. The Z n 1-form symmetry in the generalized Kitaev model 9 B. Bordism classification of anomalies 9C. Mixed anomalies between 0-form and 1-form symmetries from symmetry fractionalization 11
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.006 | 0.002 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.948 | 0.897 |
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".