Phase diagram of the SO(<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>n</mml:mi></mml:math>) bilinear-biquadratic chain from many-body entanglement
Bibliographic record
Abstract
Here we investigate the phase diagram of the SO($n$) bilinear-biquadratic quantum spin chain by studying the global quantum correlations of the ground state. We consider the cases of $n=3,\phantom{\rule{0.28em}{0ex}}4$, and 5 and focus on the geometric entanglement in the thermodynamic limit. Apart from capturing all the known phase transitions for these cases, our analysis shows a number of distinctive behaviors in the phase diagrams which we conjecture to be general and valid for arbitrary $n$. In particular, we provide an intuitive argument in favor of an infinite entanglement length in the system at a purely biquadratic point. Our results are also compared to those of other methods, such as fidelity diagrams.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 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".