XCube — model index
Fracton X-cube model on the 3-D cubic lattice (Vijay-Haah-Fu 2016) — prototype of Type-I fracton topological order with subextensive ground-state degeneracy that scales linearly with each lattice direction.
Generated by docs/atlas/generate.jl — a pure VIEW over the *_registry.jl claims + the static test/INVENTORY.jsonl AST scan. No test is executed and no src is run; test/INVENTORY.jsonl is regenerated in-place (idempotently) from that static scan; fetch/@register untouched. Assurance labels are PROVISIONAL: residuals / confidence are not shown yet (RES not wired). Badges reflect the committed test AST, not the latest CI run — a hub can read green while its @test is red between regenerations. @sweep = a graceful regime-resolution gap, not card omission.
All (Quantity, BC) hubs src claims for XCube. Cells link to the per-hub card; — = not yet implemented at that BC. The shape of the matrix is the gap visualisation: empty cells are where physics could be added next.
Convention
| Field | Value |
|---|---|
| Hamiltonian | Stabilizer / operator product |
| Observable | Operator-product expectations (Wilson loops, GSD, TEE, S-matrix entries); convention-free |
| Reference | docs/src/conventions.md §Topological / operator-product |
Coverage
| Level | Count |
|---|---|
| 🟣 universality-corroborated | 0 |
| 🟢 corroborated-at-p | 1 |
| 🔵 coherent | 0 |
| ⚪ cited-only | 0 |
| 🟠 uncorroborated-but-feasible | 0 |
| total claimed hubs | 1 |
This model is in ED_INFEASIBLE_MODELS (true 2D / frontier). Its cited-only hubs are the published ceiling, not an actionable gap.
Methods (from @register, derived): analytic
Quantity × BC matrix
| Quantity | PBC |
|---|---|
GroundStateDegeneracy | 🟢 hub |
References
Papers cited by this model's @register cards. The full numbered list is on the Reference List.
- [12]
- K. Slagle and Y. B. Kim. Quantum field theory of X-cube fracton topological order and robust degeneracy from geometry. Physical Review B 96 (2017).
- [13]
- S. Vijay, J. Haah and L. Fu. Fracton topological order, generalized lattice gauge theory, and duality. Physical Review B 94 (2016).