Bibliographic record
Abstract
The increased ability to engineer two-dimensional (2D) systems, either using materials, photonic lattices, or cold atoms, has led to the search for 2D structures with interesting properties.One such property is the presence of flat bands.Typically, the presence of these requires long-ranged hoppings, finetuning of nearest neighbor hoppings, or breaking time-reversal symmetry by using a staggered flux distribution in the unit cell.We provide a prescription based on carrying out projections from a parent system to generate different flat band systems.We identify the conditions for maintaining the flatness and identify a path-exchange symmetry in such systems that cause the flat band to be degenerate with the other dispersive ones.Breaking this symmetry leads to lifting the degeneracy while still preserving the flatness of the band.This technique does not require changing the topology nor breaking time-reversal symmetry as was suggested earlier in the literature.The prescription also eliminates the need for any fine-tuning.Moreover, it is shown that the subsequent projected systems inherit the precise fine-tuning conditions that were discussed in the literature for similar systems, in order to have and isolate a flat band.As examples, we demonstrate the use of our prescription to arrive at the flat band conditions for popular systems like the Kagomé, the Lieb, and the Dice lattices.Finally, we are also able to show that a flat band exists in a recently proposed chiral spin-liquid state of the Kagomé lattice only if it is associated with a gauge field that produces a flux modulation of the Chern-Simons type.4 A prescription to generate flat band systems 11 4.1 Flat bands beyond the bipartite condition 14 5 Isolating the flat band 16 6 Application of the prescription to other lattices 18 6.1 Lieb lattice and its projections 19 6.2 Dice lattice and its projections 21 7 Flat band with Chern-Simons flux distribution 23 8 Conclusion 26 A Useful relations between matrix elements αi 27 B Properties of non-square matrices 28 C Identifying the path-exchange symmetry 28 References 29
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.006 | 0.002 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.954 | 0.898 |
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".