We use the exceptional point in Hopfield-Bogoliubov matrix to find phase transition points bosonic system. In many previous jobs, excitation energy vanished at critical point. It can be stated equivalently that quantum is obtained when determinant of vanishes. analytically obtain corresponding general quadratic Hamiltonian. For single-mode system appearance equivalent disappearance matrix. Howe...

Dynamical phase transition (DPT) characterizes the abrupt change of dynamical properties in nonequilibrium quantum many-body systems. It has been demonstrated that extra fluctuating modes besides conventional order parameter field can drastically equilibrium transitions. However, counterpart phenomena DPTs have rarely explored. Here, we study DPT Dirac system after a sudden quench, and find fer...