Supported models and calculations¶
First calculation · Tutorials · Arithmetic and execution capabilities
Choose a physical calculation here, then follow its guide for the Hamiltonian, normalization, allowed sectors and numerical controls. An implemented model usually covers selected state families, not its complete spectrum. The model roadmap discusses further integrable models and extensions; those proposals are separate from the supported calculations below.
Current coverage¶
Program names below omit the bethe- prefix: xxx-pbc means
bethe-xxx-pbc. pbc means periodic boundaries; obc means the open-boundary
problem specified by that guide. Dispersion, continuum and finite-size tools
answer different questions. All numerical frontends support explicit MPFR in
an enabled build; inspect bethe-info for the formats actually configured.
Spin chains¶
| Family | Programs | Supported calculation and reference | Plotted tutorial |
|---|---|---|---|
| XXX | xxx-pbc, xxx-obc, xxx-structure-factor, xxx-structure-factor-thermo, xxx-moments-thermo |
Family guide: ground/sector minima, selected real-root excitations, finite-ring two-spinon intensities, selected thermodynamic spectra and direct moments | Finite chains, spectral weights, thermodynamic intensity |
| XXZ | xxz-pbc, xxz-obc, xxz-dispersion, xxz-structure-factor-thermo |
Family guide: anisotropic finite-chain states and zero-field gapless/massive spinons, continuum edges and massive transverse two-spinon intensity | Spinons and continua |
| Quantum-group XXZ | xxz-qg-obc |
Non-Hermitian open chain: regular real-root families; complete free-point fixed-Sz spectra and Jordan-block sizes | Non-Hermitian spectra |
| XYZ | xyz-pbc, xyz-dispersion |
Even-ring ground branch; thermodynamic spinons, bound branches and two-spinon envelopes | Bound branches |
| SU(3)/ULS | su3-pbc, su3-dispersion |
Balanced finite singlet; elementary 3/bar3 lines and two-/four-soliton bounds | ULS excitations |
| Spin-1 TB | tb-pbc, tb-dispersion |
Even-ring singlet with string deviations; spinons and two-/four-spinon bounds | TB spinons |
| Spin-1 biquadratic | biquadratic-obc |
Family guide: both signs, TL module minima, selected real/complex-root levels, ferromagnetic bands and droplets | Negative sign, ferromagnetic sign |
| Integrable ladder | ladder-pbc |
Sector minima and magnetization, with the required integrable four-spin coupling | Field response |
| Haldane–Shastry | haldane-shastry-pbc |
Exact ring energies and bounded complete motif spectra, with multiplicities | Motifs and spins |
| Three-state Potts | potts-pbc |
Periodic vacuum and selected charged one-hole levels, resolved by momentum/Z₃ charge | Charged levels and CFT |
Electrons and continuum gases¶
| Family | Programs | Supported calculation and reference | Plotted tutorial |
|---|---|---|---|
| Hubbard | hubbard-pbc, hubbard-obc, hubbard-dispersion, hubbard-continuum |
Family guide: finite ground states, half-filled/doped spin-charge lines and half-filled two-particle edges | Half filling, doping |
| Lieb–Liniger | lieb-liniger-pbc, lieb-liniger-obc, lieb-liniger-dispersion, lieb-liniger-thermal |
Repulsive rings, hard walls, type-I/II thermodynamic curves and finite-temperature equilibrium | Particle/hole branches |
| q-bosons | q-boson-pbc |
Fixed-particle-number ground states and canonical excitation scans, including free and phase-model limits | Deformation and limits |
| Gaudin–Yang | gaudin-yang-pbc |
Repulsive two-component gas, interacting odd-population shells and free/polarized limits | Repulsion and roots |
| Supersymmetric t–J | tj-pbc |
Sector ground states at J=2t, supported doped shells and no-hole/polarized sectors | Fillings and limits |
| SU(n) fermion gas | sun-fermions-pbc |
Repulsive multicomponent ground states, odd occupied populations and free/single-component limits | Components and seas |
| Bose–Fermi mixture | bose-fermi-pbc |
Equal-mass/equal-coupling repulsive ground states, supported mixed shells and pure/free limits | Composition benchmarks |
| Sutherland | sutherland-pbc |
Exact bosonic ground/excited energies, specified labels and bounded label windows | Collision branches |
Pairing and impurities¶
| Family | Programs | Supported calculation and reference | Plotted tutorial |
|---|---|---|---|
| Richardson pairing | richardson |
Attractive reduced-BCS ground states, distinct levels and specified paired/blocked sector | Pairing and blocking |
| Central spin | central-spin |
Spin-1/2 sector minima, distinct nonzero bath couplings and a central field | Field response |
| Kondo | kondo-response |
Zero-temperature scaling-limit impurity energy change, magnetization and susceptibility | Impurity response |
Field theory¶
| Family | Programs | Supported calculation and reference | Plotted tutorial |
|---|---|---|---|
| Sine-Gordon | sine-gordon-vacuum, sine-gordon-excited, sine-gordon-dispersion, sine-gordon-bethe-yang |
Finite-volume vacuum, selected exact two-hole levels, and particle lines, thresholds and asymptotic Bethe–Yang pairs | Particles and finite volume |
| Scaling Lee–Yang | lee-yang-vacuum, lee-yang-excited |
Periodic vacuum and regular zero-momentum one-particle branch | Vacuum and gap |
Stochastic systems¶
| Family | Programs | Supported calculation and reference | Plotted tutorial |
|---|---|---|---|
| TASEP | tasep-pbc |
Leading relaxation branch on a periodic ring at arbitrary filling | Relaxation and scaling |
| ASEP | asep-pbc |
Bidirectional relaxation branch, unequal rates and the symmetric limit | Bias and symmetry |
These tools return stochastic rates/decay eigenvalues, not quantum energies.
Further models and specialized methods¶
The roadmap and literature survey retains proposed models, original implementation slices, reference sources and remaining extensions. Specialized APIs and numerical investigations are linked from the family pages; an equation being solvable does not imply a supported frontend or full spectrum.
Earlier catalogue links now lead to the candidate index, Lieb–Liniger proposal, and SU(n)/ULS proposal.