Magnetically stabilized nematic order: Three-dimensional bipartite optical lattices
Bibliographic record
Abstract
We study magnetically stabilized nematic order for spin-one bosons in optical lattices. We show that the Zeeman field-driven quantum phase transitions between non-nematic Mott states and quantum spin nematic Mott states in the weak hopping limit are in the universality class of the ferromagnetic $XXZ$ $(S=1∕2)$ spin model. We further discuss these transitions as condensation of interacting magnons. The development of O(2) nematic order when external fields are applied corresponds to condensation of magnons, which breaks a U(1) symmetry. Microscopically, this results from a coherent superposition of two non-nematic states at each individual site. Nematic order and spin-wave excitations around critical points are studied and critical behaviors are obtained in a dilute gas approximation. We also find that spin-singlet states are unstable with respect to quadratic Zeeman effects and Ising nematic order appears in the presence of any finite quadratic Zeeman coupling. All discussions are carried out for states in three-dimensional bipartite lattices.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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) | 0.001 | 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 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".