Tutorials and model coverage¶

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These worked examples connect actual solver exports to physical questions. They include plots, downloadable data, reproduction scripts, normalization checks and caveats for interpreting the result. Start with XXZ spinons for the export-and-plot workflow, then choose a model below.

Running the examples¶

Commands use bethe-* names on PATH, not a particular build or install directory. If you are working directly in your build directory, either prepend ./ to those names or add that directory to PATH as described in the build guide. Run calculations wherever you want their output files; the source checkout is not required.

The optional figure-reproduction commands are different: run python3 scripts/… from the source checkout, with the plotting dependencies installed. A single-tool script accepts --solver bethe-… from PATH or an explicit executable path. Multi-tool scripts take an executable directory via --solver-dir (or the documented --bin-dir/--build-dir option): replace /path/to/bethe/bin with your actual build or installed binary directory; it need not be named bin. Without these options, scripts read the checked-in data. Regeneration replaces the repository's example data, not files in your calculation directory.

For arithmetic and convergence choices, use the numerical accuracy guide. It distinguishes working precision, stopping criteria and the errors that remain after a solver reports success.

Suggested starting paths¶

• First Bethe calculation: four-site XXX, then finite-chain excitations and precision.
• MPS/iMPS excitation comparisons: XXZ spinons, Hubbard spin/charge lines, then the relevant model guide for normalization and supported families.
• Spectral intensity: finite XXX two-spinon weights and the thermodynamic density, then four-spinon refinement, six-spinon sampling, then the combined 2/4/6 reference comparison. Large-domain reference regeneration is optional; the small examples teach the commands without requiring the production calculation.

Available tutorials¶

Spin chains¶

• XXX: finite-ring spinons and periodic/free-end excitation scans.
• XXX precision: resolving small energy scales, stable formulas and arbitrary precision.
• XXX spectral weights: two-spinon intensities, sum rules and plotting broadening.
• Thermodynamic XXX intensity: exact two-spinon spectral density without broadening.
• Four-spinon refinement: separate order/cutoff checks, measured cost and a small six-spinon sampling example.
• Six-spinon sampling: small worked examples, physical proposals, replicate errors, precision and soft-domain checks.
• Two-, four- and six-spinon reference comparison: interpreting saved sector contributions and partial sums, with optional production regeneration.
• XXZ spinons and continua: gapless/gapped bands and two-site folding.
• XYZ: gapped spinons, bound branches and discrete parity copies.
• SU(3)/ULS: representations, two-/four-soliton thresholds and three-site folding.
• Takhtajan–Babujian: spin selection rules and quadrupolar continua.
• Negative biquadratic chain: TL sectors, spin multiplicities and complex-root singlets.
• Ferromagnetic biquadratic chain: one-defect bands and bound droplets.
• Haldane–Shastry: motifs, spin multiplicities and complete finite spectra.
• Three-state Potts: charged branches, discrete symmetries and finite-size CFT estimators.
• Non-Hermitian XXZ: regular-root families, Jordan blocks and parity-dependent Casimir terms.
• Integrable ladder: field envelopes, magnetization steps and highest-weight descendants.

Electrons and gases¶

• Hubbard at half filling: spin–charge separation and energy conventions.
• Doped Hubbard: gapless charge branches and chemical-potential subtraction.
• Lieb–Liniger: particle/hole branches and density scaling.
• q-bosons: occupation-dependent hopping from free bosons to the phase limit.
• Gaudin–Yang: repulsion, nested roots and finite-ring shell conventions.
• Supersymmetric t–J: selected dopings, projected fermions and the no-hole XXX limit.
• SU(n) fermions: component populations, nested seas and cross-model reductions.
• Bose–Fermi mixtures: equal-coupling composition benchmarks and particle statistics.
• Sutherland: collision exponents, excitation labels and bounded scans.

Pairing and impurities¶

• Richardson pairing: blocked sectors and regular variables through pair-root collisions.
• Central spin: fixed-sector field response and energy-derived central polarization.
• Kondo: host subtraction, susceptibility calibration and universal impurity response.

Field theory¶

• Sine-Gordon: breather thresholds and exact versus asymptotic finite-volume gaps.
• Scaling Lee–Yang: effective central charge and a nonunitary one-particle gap.

Stochastic systems¶

• TASEP: relaxation times, oscillation and density-dependent size scaling.
• ASEP: a fixed-total-rate bias scan and the symmetric limit.

Coverage of implemented models¶

Every implemented model family has a worked tutorial: Hubbard has separate half-filled/doped examples and XXX has energies, spectral weights and a high-precision example. This inventory includes finite systems and impurity response, not only thermodynamic excitation tools. Proposed but unimplemented models in the model roadmap are outside this inventory.

A model tutorial introduces a useful supported calculation; it does not imply that every frontend mode or every physical sector is implemented. Boundary conditions, finite-size solvers, thermal modes and specialised spectrum searches remain documented in their linked reference guides and can support additional tutorials as the collection grows.

Reproducibility and publication¶

Each completed tutorial must have runnable commands, stated energy/momentum conventions, checked numerical exports, interpretation of the result and links to the literature. Where figures are used, their scripts read the exports rather than silently substituting an independent model calculation.

Major additions are committed, pushed and published to GitHub Pages, with checks of the deployed pages. Numerical data and figures are regenerated explicitly; ordinary site builds do not compile the solvers. See maintaining tutorials for the workflow.