Why this work is in the frame
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Bibliographic record
Abstract
We explore the possible particle-hole instabilities that can arise in a system of massless Dirac fermions on both the honeycomb and $\ensuremath{\pi}$-flux square lattices with short range interactions. Through analytical and numerical studies we show that these instabilities can result in a number of interesting phases. In addition to the previously identified charge and spin density wave phases and the exotic ``quantum anomalous Hall'' (Haldane) phase, we establish the existence of the dimerized ``Kekul\'e'' phase over a significant portion of the phase diagram and discuss the possibility of its spinful counterpart, the ``spin Kekul\'e'' phase. On the $\ensuremath{\pi}$-flux square lattice we also find various stripe phases, which do not occur on the honeycomb lattice. The Kekul\'e phase is described by a ${\text{Z}}_{3}$ order parameter whose singly quantized vortices carry fractional charge $\ifmmode\pm\else\textpm\fi{}e/2$. On the $\ensuremath{\pi}$-flux lattice the analogous dimerized phase is described by a ${\text{Z}}_{4}$ order parameter. We perform a fully self-consistent calculation of the vortex structure inside the dimerized phase and find that close to the core the vortex resembles a familiar superconducting U(1) vortex, but at longer length scales a clear ${Z}_{4}$ structure emerges with domain walls along the lattice diagonals.
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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 | 0.000 | 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 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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 it