Report on scipost_202204_00018v1
Bibliographic record
Abstract
Progress in understanding symmetry-protected topological (SPT) phases has been greatly aided by our ability to construct lattice models realizing these states.In contrast, a systematic approach to constructing models that realize quantum critical points between SPT phases is lacking, particularly in dimension d > 1.Here, we show how the recently introduced notion of the pivot Hamiltonian-generating rotations between SPT phases-facilitates such a construction.We demonstrate this approach by constructing a spin model on the triangular lattice, which is midway between a trivial and SPT phase.The pivot Hamiltonian generates a U (1) pivot symmetry which helps to stabilize a direct SPT transition.The sign-problem free nature of the model-with an additional Ising interaction preserving the pivot symmetry-allows us to obtain the phase diagram using quantum Monte Carlo simulations.We find evidence for a direct transition between trivial and SPT phases that is consistent with a deconfined quantum critical point with emergent SO(5) symmetry.The known anomaly of the latter is made possible by the non-local nature of the U (1) pivot symmetry.Interestingly, the pivot Hamiltonian generating this symmetry is nothing other than the staggered Baxter-Wu three-spin interaction.This work illustrates the importance of U (1) pivot symmetries and proposes how to generally construct sign-problem-free lattice models of SPT transitions with such anomalous symmetry groups for other lattices and dimensions.4.1.2The Union Jack lattice 14 4.2 Z 4 2 or Z 3 2 × Z T 2 SPT on the BCC lattice 15 4.3 Subsystem SPT in 3D 16 5 Outlook 17 A Details of the cluster algorithm 18 B More numerical results 20 C Other direct transitions in 2D 22 D Generalized XY models in 3D 23 D.1 Dual of the 3D SPT: color code topological order 23 D.2 Dual of the 3D SSPT: Checkerboard fracton order 24 References 25
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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".