Report on scipost_202204_00017v1
Bibliographic record
Abstract
It is well-known that symmetry-protected topological (SPT) phases can be obtained from the trivial phase by an entangler, a finite-depth unitary operator U .Here, we consider obtaining the entangler from a local 'pivot' Hamiltonian H pivot such that U = e iπH pivot .This perspective of Hamiltonians pivoting between the trivial and SPT phase opens up two new directions: (i) Since SPT Hamiltonians and entanglers are now on the same footing, can we iterate this process to create other interesting states?(ii) Since entanglers are known to arise as discrete symmetries at SPT transitions, under what conditions can this be enhanced to U (1) pivot symmetry generated by H pivot ?In this work we explore both of these questions.With regard to the first, we give examples of a rich web of dualities obtained by iteratively using an SPT model as a pivot to generate the next one.For the second question, we derive a simple criterion for when the direct interpolation between the trivial and SPT Hamiltonian has a U (1) pivot symmetry.We illustrate this in a variety of examples, assuming various forms for H pivot , including the Ising chain, and the toric code Hamiltonian.A remarkable property of such a U (1) pivot symmetry is that it shares a mutual anomaly with the symmetry protecting the nearby SPT phase.We discuss how such anomalous and non-onsite U (1) symmetries explain the exotic phase diagrams that can appear, including an SPT multicritical point where the gapless ground state is given by the fixed-point toric code state.A Technical details about 1D models 23 A.1 Proof of U (1) pivot symmetry 23 A.2 Field theory of the SPT transition 24 A.3 KT multicritical point 24 A.4 Kramers-Wannier duality: making the pivot local 25 B Sufficient condition for enhanced U (1) symmetry 25 C Pivots from decorated domain walls 27 D Exactly-solvable path 28
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.158 | 0.002 |
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".