Many topological regions on the Bloch sphere of the spin-1/2 double-kicked top
Bibliographic record
Abstract
Floquet topological systems have been shown to exhibit features not commonly found in conventional topological systems such as topological phases characterized by arbitrarily large winding numbers. This is clearly highlighted in the quantum double kicked rotor coupled to spin-1/2 degrees of freedom [Phys. Rev. A 97, 063603 (2018)] where large winding numbers are achieved by tuning the kick strengths. Here, we extend the results to the spin-1/2 quantum double kicked top and find not only does the system exhibit topological regions with large winding numbers, but a large number of them are needed to fully characterize the topology of the Bloch sphere of the top for general kick strengths. Due to the geometry of the Bloch sphere it is partitioned into regions with different topology and the boundaries separating them are home to 0 and $\ensuremath{\pi}$ quasienergy bound states. We characterize the regions by comparing local versions of the mean field, quantum, and mean chiral displacement winding numbers. We also use a probe state to locate the boundaries by observing localization as the state evolves when it has a large initial overlap with bound states. Finally, we briefly discuss the connections between the spin-1/2 quantum double kicked top and multistep quantum walks, putting the system in the context of some current experiments in the exploration of topological phases.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.003 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".