  We investigate the transition from PT-symmetry to PT-symmetry breaking and
vice versa in the non-Hermitian Landau-Zener (LZ) models. The energy is
generally complex, so the relaxation rate of the system is set by the absolute
value of the gap. To illustrate the dynamics of phase transitions, the relative
population is introduced to calculate the defect density in nonequilibrium
phase transitions instead of the excitations in the Hermitian systems. The
result shows that the adiabatic-impulse (AI) approximation, which is the key
concept of the Kibble-Zurek (KZ) mechanism in the Hermitian systems, can be
generalized to the PT-symmetric non-Hermitian LZ models to study the dynamics
in the vicinity of a critical point. Therefore, the KZ mechanism in the
simplest non-Hermitian two-level models is presented. Finally, an exact
solution to the non-Hermitian LZ-like problem is also shown.
