Nonsymmorphic spin-space cubic groups and SU(2)$_1$ conformal invariance in one-dimensional spin-1/2 models
Bibliographic record
Abstract
Recently, extended gapless phases with emergent SU(2) _1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi/> <mml:mn>1</mml:mn> </mml:msub> </mml:math> conformal invariance occupying finite regions in the phase diagrams have been found in one-dimensional spin-1/2 models with nonsymmorphic O_h <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>O</mml:mi> <mml:mi>h</mml:mi> </mml:msub> </mml:math> symmetry groups. In this work, we investigate the question of whether the conditions for emergent SU(2) _1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi/> <mml:mn>1</mml:mn> </mml:msub> </mml:math> invariance can be loosened. We find that besides the nonsymmorphic O_h <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>O</mml:mi> <mml:mi>h</mml:mi> </mml:msub> </mml:math> group, the other four smaller nonsymmorphic cubic groups including O <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>O</mml:mi> </mml:math> , T_h <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>h</mml:mi> </mml:msub> </mml:math> , T_d <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>d</mml:mi> </mml:msub> </mml:math> and T <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>T</mml:mi> </mml:math> can also give rise to emergent SU(2) _1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi/> <mml:mn>1</mml:mn> </mml:msub> </mml:math> invariance. Minimal spin-1/2 models having these nonsymmorphic cubic groups as symmetry groups are constructed, and numerical evidences for the emergent SU(2) _1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi/> <mml:mn>1</mml:mn> </mml:msub> </mml:math> invariance are provided. Our work is useful for understanding gapless phases in one-dimensional spin systems with nonsymmorphic symmetries.
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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 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 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".