Unusual excitations and double-peak specific heat in a bond-alternating spin-1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>K</mml:mi><mml:mo>−</mml:mo><mml:mi mathvariant="normal">Γ</mml:mi></mml:math> chain
Bibliographic record
Abstract
One-dimensional gapped phases that avoid any symmetry breaking have drawn enduring attention. In this paper, we study such phases in a bond-alternating spin-1 $K\ensuremath{-}\mathrm{\ensuremath{\Gamma}}$ chain built of a Kitaev ($K$) interaction and an off-diagonal $\mathrm{\ensuremath{\Gamma}}$ term. In the case of isotropic bond strength, a Haldane phase, which resembles the ground state of a spin-1 Heisenberg chain, is identified in a wide region. A gapped Kitaev phase situated at dominant ferromagnetic and antiferromagnetic Kitaev limits is also found. The Kitaev phase has extremely short range spin correlations and is characterized by finite ${\mathbb{Z}}_{2}$-valued quantities on bonds. Its lowest entanglement spectrum is unique, in contrast to the Haldane phase, whose entanglement spectrum is doubly degenerate. In addition, the Kitaev phase shows a double-peak structure in the specific heat at two different temperatures. In the pure Kitaev limit, the two peaks are representative of the development of short-range spin correlation at ${T}_{h}\ensuremath{\simeq}0.5680$ and the freezing of ${\mathbb{Z}}_{2}$ quantities at ${T}_{l}\ensuremath{\simeq}0.0562$, respectively. By considering bond anisotropy, regions of Haldane phase and Kitaev phase are enlarged, accompanied by the emergence of dimerized phases and three distinct magnetically ordered states.
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 0.002 |
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; both teacher heads agree on what is shown here.
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".