AKLT1D — model index
Spin-1 bilinear-biquadratic chain at the AKLT point,
H = J Σᵢ [ Sᵢ · Sᵢ₊₁ + (1/3) (Sᵢ · Sᵢ₊₁)² ],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 AKLT1D. 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 | Spin S (this file) |
| Observable | Spin S (QAtlas-wide spin convention; see docs/src/conventions.md) |
Coverage
| Level | Count |
|---|---|
| 🟣 universality-corroborated | 0 |
| 🟢 corroborated-at-p | 17 |
| 🔵 coherent | 0 |
| ⚪ cited-only | 1 |
| 🟠 uncorroborated-but-feasible | 1 |
| total claimed hubs | 19 |
Methods (from @register, derived): analytic, dense_ed, literature_value
Quantity × BC matrix
| Quantity | OBC | PBC | Infinite |
|---|---|---|---|
CorrelationLength | — | — | 🟢 hub |
Energy | — | — | 🟢 hub |
ExactSpectrum | 🟠 hub | — | — |
FreeEnergy | 🟢 hub | 🟢 hub | 🟢 hub |
GroundStateEnergyDensity | — | — | 🟢 hub |
MassGap | — | — | ⚪ hub |
SpecificHeat | 🟢 hub | 🟢 hub | 🟢 hub |
StringOrderParameter | — | — | 🟢 hub |
SusceptibilityZZ | — | 🟢 hub | 🟢 hub |
ThermalEntropy | 🟢 hub | 🟢 hub | 🟢 hub |
ZZCorrelation | — | — | 🟢 hub |
ZZStructureFactor | — | — | 🟢 hub |
References
Papers cited by this model's @register cards. The full numbered list is on the Reference List.
- [55]
- I. Affleck, T. Kennedy, E. H. Lieb and H. Tasaki. Valence bond ground states in isotropic quantum antiferromagnets. Communications in Mathematical Physics 115, 477–528 (1988).
- [56]
- D. P. Arovas and A. Auerbach. Extended Heisenberg models of antiferromagnetism: Analogies to the fractional quantum Hall effect. Physical Review Letters 60, 531–534 (1988).
- [57]
- A. Garcia-Saez, V. Murg and T.-C. Wei. Spectral gaps of Affleck-Kennedy-Lieb-Tasaki Hamiltonians using tensor network methods. Physical Review B 88, 245118 (2013), arXiv:1308.3631.
- [58]
- T. Kennedy and H. Tasaki. Hidden $Z_2 \times Z_2$ symmetry breaking in Haldane-gap antiferromagnets. Physical Review B 45, 304–307 (1992).