Fermion decoration construction of symmetry-protected trivial order for fermion systems with any symmetry and in any dimension
Bibliographic record
Abstract
We use higher-dimensional bosonization and fermion decoration to construct exactly soluble interacting fermion models to realize fermionic symmetry-protected trivial (SPT) orders (which are also known as symmetry-protected topological orders) in any dimensions and for generic fermion symmetries ${G}_{f}$, which can be a nontrivial ${Z}_{2}^{f}$ extension ${Z}_{2}^{f}\ensuremath{\leftthreetimes}{G}_{b}$ (where ${Z}_{2}^{f}$ is the fermion-number-parity symmetry and ${G}_{b}$ is the bosonic symmetry). This generalizes the previous results from group supercohomology of Gu and Wen (arXiv:1201.2648), where ${G}_{f}$ is assumed to be ${Z}_{2}^{f}\ifmmode\times\else\texttimes\fi{}{G}_{b}$. We find that the $(d+1)$-dimensional $[(d+1)\mathrm{D}]$ fermionic SPT phases with bosonic symmetry ${G}_{b}$ and from fermion decoration construction can be described in a compact way using higher group homomorphism: $\mathcal{B}{G}_{b}\stackrel{\ensuremath{\varphi}}{\ensuremath{\rightarrow}}\mathcal{B}({Z}_{2},2;{Z}_{2},d)$. In fact, the fermion symmetry is more precisely described by the structure ${Z}_{2}^{f}\ensuremath{\leftthreetimes}{G}_{b}\ensuremath{\leftthreetimes}S{O}_{\ensuremath{\infty}}$ (or ${Z}_{2}^{f}\ensuremath{\leftthreetimes}{G}_{b}\ensuremath{\leftthreetimes}{O}_{\ensuremath{\infty}}$ with time-reversal symmetry). In this case the $(d+1)\mathrm{D}$ fermionic SPT phases are better described by $\mathcal{B}({Z}_{2}^{f}\ensuremath{\leftthreetimes}{G}_{b}\ensuremath{\leftthreetimes}S{O}_{\ensuremath{\infty}})\stackrel{\ensuremath{\varphi}}{\ensuremath{\rightarrow}}\mathcal{B}(S{O}_{\ensuremath{\infty}},1;{Z}_{2},d)$ [or $\mathcal{B}({Z}_{2}^{f}\ensuremath{\leftthreetimes}{G}_{b}\ensuremath{\leftthreetimes}{O}_{\ensuremath{\infty}})\stackrel{\ensuremath{\varphi}}{\ensuremath{\rightarrow}}\mathcal{B}({O}_{\ensuremath{\infty}},1;{Z}_{2},d)]$.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| 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".