XXZ1D — model index
The spin-$\tfrac12$ XXZ chain — the uniaxially anisotropic Heisenberg model, Bethe-ansatz integrable, with a critical Luttinger-liquid line for $-1 < \Delta \le 1$.
\[H = \sum_i \left( S^x_i S^x_{i+1} + S^y_i S^y_{i+1} + \Delta\, S^z_i S^z_{i+1} \right)\]
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 XXZ1D. 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 | 18 |
| 🔵 coherent | 5 |
| ⚪ cited-only | 0 |
| 🟠 uncorroborated-but-feasible | 9 |
| total claimed hubs | 32 |
Methods (from @register, derived): analytic, bethe_ansatz, delegation, dense_ed, exact_2spinon, free_fermion_analytic, free_fermion_quadgk_or_klumper_nlie, klumper_nlie
Quantity × BC matrix
Derivation notes
Matched by filename substring (no annotation; substrate-derived):
ad-thermodynamics-from-z.mdcalabrese-cardy-obc-vs-pbc.mdxx-quench.mdxxz-luttinger-parameters.mdyang-magnetization-toeplitz.md
References
Papers cited by this model's @register cards. The full numbered list is on the Reference List.
- [32]
- P. Calabrese and J. Cardy. Entanglement entropy and quantum field theory. Journal of Statistical Mechanics: Theory and Experiment 2004, P06002 (2004).
- [34]
- P. Calabrese, F. H. Essler and M. Fagotti. Quantum quench in the transverse field Ising chain: I. Time evolution of order parameter correlators. Journal of Statistical Mechanics: Theory and Experiment 2012, P07016 (2012).
- [186]
- R. Chitra and T. Giamarchi. Critical properties of gapped spin-chains and ladders in a magnetic field. Physical Review B 55, 5816–5826 (1997).
- [111]
- P. Coleman. Introduction to Many-Body Physics (Cambridge University Press, 2015).
- [127]
- F. H. Essler and M. Fagotti. Quench dynamics and relaxation in isolated integrable quantum spin chains. Journal of Statistical Mechanics: Theory and Experiment 2016, 064002 (2016).
- [110]
- T. Giamarchi. Quantum Physics in One Dimension (Oxford University Press, 2003).
- [39]
- M. Heyl, A. Polkovnikov and S. Kehrein. Dynamical Quantum Phase Transitions in the Transverse-Field Ising Model. Physical Review Letters 110 (2013).
- [87]
- L. Hulthén. Über das Austauschproblem eines Kristalles. Arkiv för Matematik, Astronomi och Fysik 26A, 1–106 (1938).
- [105]
- A. Klümper. Thermodynamics of the anisotropic spin-1/2 Heisenberg chain and related quantum chains. Zeitschrift für Physik B Condensed Matter 91, 507–519 (1993).
- [112]
- G. D. Mahan. Many-Particle Physics (Springer US, 2000).
- [184]
- I. Pérez Castillo. The exact two-spinon longitudinal dynamical structure factor of the anisotropic XXZ model (2020), arXiv:2005.10729 [cond-mat.str-el].
- [109]
- M. Takahashi. Thermodynamics of One-Dimensional Solvable Models (Cambridge University Press, 1999).
- [94]
- C. N. Yang and C. P. Yang. One-Dimensional Chain of Anisotropic Spin-Spin Interactions. II. Properties of the Ground-State Energy Per Lattice Site for an Infinite System. Physical Review 150, 327–339 (1966).
- [136]
- C. N. Yang and C. P. Yang. Thermodynamics of a One-Dimensional System of Bosons with Repulsive Delta-Function Interaction. Journal of Mathematical Physics 10, 1115–1122 (1969).
- [90]
- J. des Cloizeaux and J. J. Pearson. Spin-Wave Spectrum of the Antiferromagnetic Linear Chain. Physical Review 128, 2131–2135 (1962).