  The Richardson-Gaudin model describes strong pairing correlations of fermions
confined to a finite chain. The integrability of the Hamiltonian allows for its
eigenstates to be constructed algebraically. In this work we show that quantum
group theory provides a possibility to deform the Hamiltonian while preserving
integrability. More precisely, we use the so-called Jordanian r-matrix to
deform the Hamiltonian of the Richardson-Gaudin model. In order to preserve its
integrability, we need to insert a special nilpotent term into the auxiliary
L-operator which generates integrals of motion of the system. Moreover, the
quantum inverse scattering method enables us to construct the exact eigenstates
of the deformed Hamiltonian. These states have a highly complex entanglement
structure which requires further investigation.
