<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>S</mml:mi><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mn>8</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math> unification and the large-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math> theory of superconductor-insulator transition of two-dimensional Dirac fermions
Bibliographic record
Abstract
Electrons on honeycomb or pi-flux lattices obey the effective massless Dirac equation at low energies and at the neutrality point, and should suffer quantum phase transitions into various Mott insulators and superconductors at strong two-body interactions. We show that 35 out of 36 such order parameters that provide Lorentz-invariant mass gaps to Dirac fermions belong to a single irreducible tensor representation of the $SO(8)$ symmetry of the two-dimensional Dirac Hamiltonian for the spin-1/2 lattice fermions. The minimal interacting Lagrangian away from the neutrality point has the $SO(8)$ symmetry reduced to $U(1)\ifmmode\times\else\texttimes\fi{}SU(4)$ by finite chemical potential, and it allows only two independent interaction terms. When the Lagrangian is nearly $SO(8)$ symmetric and the ground state insulating at the neutrality point, we show it turns superconducting at the critical value of the chemical potential through a ``flop'' between the tensor components, by exactly solving the $SU(4)\ensuremath{\rightarrow}SU(N)$ generalization in the large-$N$ limit. A lattice Hamiltonian that may exhibit this transition, parallels with and the consequences for the Gross-Neveu model, and applicability to related electronic systems are briefly discussed.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.004 | 0.002 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.001 | 0.004 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.011 | 0.004 |
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".