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.
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