Something interacting and solvable in 1d

Understand

We present a two-parameter family of exactly solvable quantum many-body systems in one spatial dimension containing the Lieb-Liniger model of interacting bosons as a particular case.

• The principal building block of this construction is the previously-introduced (arXiv:1712.09375) family of two-particle scattering matrices.
• We discuss an $SL(2)$ transformation connecting the models within this family and make a correspondence with generalized point interactions.
• The Bethe equations for the ground state are discussed with a special emphasis on "non-interacting modes" connected by the modular subgroup of $SL(2)$.