Observations on the Bethe ansatz solutions of the spin-1/2 isotropic anti-ferromagnetic Heisenberg chain: the chiral string conjecture
Bibliographic record
Abstract
Abstract Calculations of low lying excited states in even length L → ∞ chains begun in 2019 J. Phys. Commun. 3 025007 in the total spin S = 0 sector are here extended to S > 0. Bethe string configurations that were observed to transition from their definition at small L to different ‘apparent’ configurations at large L are now understood to be a manifestation of the approximate chiral symmetry that develops with increasing chain length. It is conjectured that when chiral symmetry is built into the configuration definitions a complete explicit labelling of all low lying excited states by strings is obtained. The structure is of the form of a product of Bethe strings defining left and right chiral states of spin sL and sR and a central complex ‘string’ necessary to bind <?CDATA ${\vec{{\rm{s}}}}_{L}$?> s ⃗ L and <?CDATA ${\vec{{\rm{s}}}}_{R}$?> s ⃗ R into total <?CDATA $\vec{S}.$?> S ⃗ . Rules based on the string content of a state yield its momentum and asymptotic energy, including the amplitude of the leading ln(L) correction.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".