Heisenberg1D — model index
The spin-$\tfrac12$ antiferromagnetic Heisenberg chain — the Bethe-ansatz-integrable model of quantum magnetism, gapless with an $SU(2)_1$ WZW critical point ($c = 1$).
\[H = J\sum_{\langle i,j\rangle} \mathbf{S}_i \cdot \mathbf{S}_j, \qquad J > 0\]
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 Heisenberg1D. 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 | 13 |
| 🔵 coherent | 4 |
| ⚪ cited-only | 0 |
| 🟠 uncorroborated-but-feasible | 11 |
| total claimed hubs | 28 |
Methods (from @register, derived): analytic, bethe_ansatz, cft, cft_low_T, delegation, dense_ed, muller_ansatz
Quantity × BC matrix
| Quantity | OBC | PBC | Infinite |
|---|---|---|---|
ConformalTower | — | 🟠 hub | — |
Energy | 🟢 hub | — | — |
EnergyLocal | 🟠 hub | — | — |
FreeEnergy | 🟢 hub | — | 🟠 hub |
GroundStateEnergyDensity | — | — | 🟢 hub |
LuttingerParameter | — | — | 🔵 hub |
MagnetizationX | 🔵 hub | — | — |
MagnetizationXLocal | 🟠 hub | — | — |
MagnetizationY | 🔵 hub | — | — |
MagnetizationYLocal | 🟠 hub | — | — |
MagnetizationZ | 🔵 hub | — | — |
MagnetizationZLocal | 🟠 hub | — | — |
MassGap | 🟢 hub | — | 🟢 hub |
RenyiEntropy | 🟢 hub | — | 🟠 hub |
SpecificHeat | 🟢 hub | — | 🟠 hub |
SusceptibilityXX | 🟢 hub | — | — |
SusceptibilityYY | 🟢 hub | — | — |
SusceptibilityZZ | 🟢 hub | — | — |
ThermalEntropy | 🟢 hub | — | 🟠 hub |
UniversalityClass | — | — | 🟠 hub |
VonNeumannEntropy | 🟢 hub | — | 🟠 hub |
ZZStructureFactor | — | — | 🟢 hub |
Derivation notes
Matched by filename substring (no annotation; substrate-derived):
ad-thermodynamics-from-z.mdbethe-ansatz-heisenberg-e0.mdcalabrese-cardy-obc-vs-pbc.mdheisenberg-dimer-singlet-triplet.mdheisenberg-spinons.mdxx-quench.mdyang-magnetization-toeplitz.md
References
Papers cited by this model's @register cards. The full numbered list is on the Reference List.
- [82]
- I. Affleck. Universal term in the free energy at a critical point and the conformal anomaly. Physical Review Letters 56, 746–748 (1986).
- [83]
- I. Affleck. Quantum spin chains and the Haldane gap. Journal of Physics: Condensed Matter 1, 3047–3072 (1989).
- [84]
- H. Bethe. Zur Theorie der Metalle. Zeitschrift f�r Physik 71, 205–226 (1931).
- [31]
- H. W. Blöte, J. L. Cardy and M. P. Nightingale. Conformal invariance, the central charge, and universal finite-size amplitudes at criticality. Physical Review Letters 56, 742–745 (1986).
- [32]
- P. Calabrese and J. Cardy. Entanglement entropy and quantum field theory. Journal of Statistical Mechanics: Theory and Experiment 2004, P06002 (2004).
- [35]
- J. L. Cardy. Operator content of two-dimensional conformally invariant theories. Nuclear Physics B 270, 186–204 (1986).
- [85]
- S. Eggert, I. Affleck and M. Takahashi. Susceptibility of the spin 1/2 Heisenberg antiferromagnetic chain. Physical Review Letters 73, 332–335 (1994).
- [86]
- F. D. Haldane. General Relation of Correlation Exponents and Spectral Properties of One-Dimensional Fermi Systems: Application to the Anisotropic $S=1/2$ Heisenberg Chain. Physical Review Letters 45, 1358–1362 (1980).
- [87]
- L. Hulthén. Über das Austauschproblem eines Kristalles. Arkiv för Matematik, Astronomi och Fysik 26A, 1–106 (1938).
- [88]
- A. Luther and I. Peschel. Calculation of critical exponents in two dimensions from quantum field theory in one dimension. Physical Review B 12, 3908–3917 (1975).
- [89]
- G. Müller, H. Thomas, H. Beck and J. C. Bonner. Quantum spin dynamics of the antiferromagnetic linear chain in zero and nonzero magnetic field. Physical Review B 24, 1429–1467 (1981).
- [90]
- J. des Cloizeaux and J. J. Pearson. Spin-Wave Spectrum of the Antiferromagnetic Linear Chain. Physical Review 128, 2131–2135 (1962).