Biquadratic chains and Temperley–Lieb sectors¶
All models · Negative-sign tutorial · Ferromagnetic-sign tutorial
bethe-biquadratic-obc covers selected states of both signs of the spin-1 pure
biquadratic chain with free ends. The auxiliary XXZ/TL equations organize the
energies; physical-spin multiplicities are additional information. A TL module
label is not automatically an SU(2) spin label.
Choose a calculation¶
| Calculation | Guide |
|---|---|
| Negative-sign ground energy, TL module minima and real-root excitations | Biquadratic chain |
| Complex-root levels and bounded small-chain spectrum searches | Open-chain Q-system |
| Targeted long-chain low-lying singlet | Two-string solver |
| Ferromagnetic ground space and exact one-defect band | Ferromagnetic sign |
| Two-, three- and four-defect bound droplets | Pairs, triples, quartets |
| Real-root scattering windows | Scattering states |
| Mixed pair/defect, triple/defect and two-pair families | Pair plus defect, triple plus defect, two pairs |
| Physical SU(2) spin content and multiplicities | Spin-content guide |
Each guide gives its frontend options, state-family restrictions, tables and failure diagnostics. These modes do not collectively assert a complete excited spectrum at arbitrary length. All frontend modes support explicit MPFR when configured, but exact multiplicity counts and labels remain integer quantities.
Interpret excitation energies¶
Changing the sign reverses the ordering of auxiliary energies; it does not turn every AF state label into the corresponding lowest ferromagnetic state. Use the physical energy and stated gap reference. Bound-cluster deviations may be much smaller than the root-coordinate spacing; the dedicated deviation fields and convergence checks matter, even when rounded roots look like an exact string. The model pages preserve the derivations and validation of each restricted family.