Bibliographic record
Abstract
The Haldane conjecture (1983), which led to a Nobel prize for Duncan Haldane, was that half-integer spin chains are gapless while integer spin chains are gapped. Haldane made this observation by a mapping onto a non-linear $\sigma$-model at large spin. Gapless behavior for half-integer spin was proven rigorously by the Affleck–Lieb–Schultz–Mattis (ALSM) theorem. Gapped behavior for integer spin was demonstrated by an exactly solvable model known as Affleck–Kennedy–Lieb–Tasaki (AKLT) model (1987, 1988). In this review article, I will review the ALSM theorem and present results on the AKLT model. An important aspect of this model is that it has decoupled spin-$1/2$’s at the two ends with open boundary conditions. This was shown, by Kennedy (1990), to extend to the regular antiferromagnetic model. The first experimental demonstration of this behavior was in a paper by Hagiwara, Katsumata, Affleck, Halperin, and Renard (1990). I will review this experiment.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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".