  A two-interacting-qubit quantum Rabi-like model with vanishing transverse
fields on the qubit-pair is studied. Independently of the coupling regime, this
model can be exactly and unitarily reduced to two independent single-spin
quantum Rabi models, where the spin-spin coupling plays the role of the
transverse field. This transformation and the analytical treatment of the
single-spin quantum Rabi model provide the key to prove the integrability of
our model. The existence of different first-order quantum phase transitions,
characterized by discontinuous two-spin magnetization, mean photon number and
concurrence, is brought to light.
