BCS-BEC crossover in a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>g</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mn>4</mml:mn></mml:msup></mml:math> excitonic magnet
Bibliographic record
Abstract
The condensation of spin-orbit-induced excitons in ${t}_{2g}^{4}$ electronic systems is attracting considerable attention. At large Hubbard $U$, antiferromagnetism was proposed to emerge from the Bose-Einstein Condensation (BEC) of triplons (${J}_{\text{eff}}=1$). Here, we show that even at intermediate $U$ regimes, the spin-orbit exciton condensation is possible leading also to staggered magnetic order. The canonical electron-hole excitations (excitons) transform into local triplon excitations at large $U$, and this BEC strong coupling regime is smoothly connected to the intermediate $U$ excitonic insulator region. We solved the degenerate three-orbital Hubbard model with spin-orbit coupling ($\ensuremath{\lambda}$) in one dimension using the density matrix renormalization group, while in two dimensions we use the Hartree-Fock approximation (HFA). Employing these techniques, we provide the full $\ensuremath{\lambda}$ versus $U$ phase diagrams for both one- and two-dimensional lattices. Our main result is that at intermediate Hubbard $U$, increasing $\ensuremath{\lambda}$ at fixed $U$ the system transitions from an incommensurate spin-density-wave metal to a Bardeen-Cooper-Schrieffer (BCS) excitonic insulator, with coherence length ${r}_{\mathrm{coh}}$ of $\mathcal{O}(a)$ and $\mathcal{O}(10a)$ in $1d$ and $2d$, respectively, with $a$ being the lattice spacing. Further increasing $\ensuremath{\lambda}$, the system eventually crosses over to the BEC limit (with ${r}_{\mathrm{coh}}\ensuremath{\ll}a$).
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.019 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), 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".