  We consider a generalized Rabi model formed by two identical qubits
interacting with a common oscillator mode. In the near resonance configuration
where the oscillator frequency is close to the transition frequency of the
qubit, we determine the ground state of the model approximately by using a
variational method and a transformation method. Both methods are shown to
provide good agreement with the exact numerical ground state for a range of
coupling strength in the ultrastrong regime. In addition, we indicate how the
accuracy of the approximation can be further improved by using perturbation
theory. We also examine the ground state entanglement between the two qubits.
By calculating the negativity, we quantify the degree of entanglement as a
function of coupling strength.
