Integrable hard-rod deformation of the Heisenberg spin chains

We present integrable models of interacting spin-1/2 chains which can be interpreted as hard-rod deformations of the XXZ Heisenberg chains. The models support multiple particle types: Dynamical hard rods of length ℓ and particles with lengths ℓ^{'}<ℓ that are immobile except for the interaction with the hard rods. We encounter a remarkable phenomenon in these interacting models: Exact spectral degeneracies across different deformations and volumes. The algebraic integrability of these systems is also treated using a recently developed formalism for medium-range integrable spin chains. We present the detailed Bethe Ansatz solution for the case ℓ=2.