Comprehensive study of the phase diagram of the spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:math> Kitaev-Heisenberg-Gamma chain
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Bibliographic record
Abstract
A central question on Kitaev materials is the effects of additional couplings on the Kitaev model, which is proposed to be a candidate for realizing topological quantum computations. However, two spatial dimensions typically suffer the difficulty of lacking controllable approaches. In this work, using a combination of powerful analytical and numerical methods available in one dimension, we perform a comprehensive study on the phase diagram of a one-dimensional version of the spin-1/2 Kitaev-Heisenberg-Gamma model in its full parameter space. A strikingly rich phase diagram is found with nine distinct phases, including four Luttinger liquid phases, a ferromagnetic phase, a Nel ordered phase, an ordered phase of distorted-spiral spin alignments, and two ordered phases, which both break a D 3 symmetry albeit in different ways, where D 3 is the dihedral group of order six. Our work paves the way for studying one-dimensional Kitaev materials and may provide hints to the physics in higher-dimensional situations.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.000 | 0.003 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it