Symmetry-protected topological phases with charge and spin symmetries: Response theory and dynamical gauge theory in two and three dimensions
Bibliographic record
Abstract
A large class of symmetry-protected topological phases (SPT) in boson/spin systems have been recently predicted by the group cohomology theory. In this work, we consider bosonic SPT states at least with charge symmetry [U(1) or Z[subscript N]] or spin-S[superscript z] rotation symmetry [U(1) or Z[subscript N]] in two (2D) and three dimensions (3D) and the surface of 3D. If both are U(1), we apply external electromagnetic field/“spin gauge field” to study the charge/spin response. For the SPT examples we consider {i.e., U[subscript c](1)⋊Z[T over 2], U[subscript s](1)×Z[T over 2], U[subscript c](1)×[U[subscript s](1)⋊Z[subscript 2]]; subscripts c and s are short for charge and spin; Z[T over 2] and Z[subscript 2] are time-reversal symmetry and π rotation about S[subscript y], respectively}, many variants of Witten effect in the 3D SPT bulk and various versions of anomalous surface quantum Hall effect are defined and systematically investigated. If charge or spin symmetry reduces to Z[subscript N] by considering charge-N or spin-N condensate, instead of the linear response approach, we gauge the charge/spin symmetry, leading to a dynamical gauge theory with some remaining global symmetry. The 3D dynamical gauge theory describes a symmetry-enriched topological phase (SET), i.e., a topologically ordered state with global symmetry which admits nontrivial ground-state degeneracy depending on spatial manifold topology. For the SPT examples we consider, the corresponding SET states are described by dynamical topological gauge theory with topological BF term and axionic Θ term in 3D bulk. In addition, the surface of SET is described by the chiral boson theory with quantum anomaly.
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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 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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".