  We analytically and numerically study the Loschmidt echo and the dynamical
order parameters in a spin chain with a deconfined phase transition between a
dimerized state and a ferromagnetic phase. For quenches from a dimerized state
to a ferromagnetic phase, we find that the model can exhibit a dynamical
quantum phase transition characterized by an associating dimerized order
parameters. In particular, when quenching the system from the Majumdar-Ghosh
state to the ferromagnetic Ising state, we find an exact mapping into the
classical Ising chain for a quench from the paramagnetic phase to the classical
Ising phase by analytically calculating the Loschmidt echo and the dynamical
order parameters. By contrast, for quenches from a ferromagnetic state to a
dimerized state, the system relaxes very fast so that the dynamical quantum
transition may only exist in a short time scale. We reveal that the dynamical
quantum phase transition can occur in systems with two broken symmetry phases
and the quench dynamics may be independent on equilibrium phase transitions.
