  We present new 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 $\ell$ and
particles with lengths $\ell'<\ell$ 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 $\ell=2$.

Statistical Mechanics;High Energy Physics - Theory;Exactly Solvable and Integrable Systems