A solvable Hamiltonian is treated within a time-dependent variational approach using four different variational states. One description is equivalent to the pnQRPA approach, while another one describes a new proton-neutron collective mode which is associated with a new phase of the nuclear system. The transition from one solution to the other is achieved through a Goldstone mode. For the quantized ground and first excited states the quasi-particle correlations, the Fermi β^- and β⁺ transition amplitude and the Ikeda sum rule have been calculated. Two of the variational states are similar to the standard pnQRPA vacuum and are used to calculate the second excited states.