Adiabatic-impulse approximation in the non-Hermitian Landau-Zener model

Abstract

In the non-Hermitian Landau-Zener models, we investigate the dynamical transition both in parity-time symmetric and symmetry-broken regimes. Taking into account the complex nature of the energy of the non-Hermitian systems, the absolute value of the gap was used to determine the relaxation rate of the system. To show the dynamics of the phase transitions, the relative population is used to estimate the topological defect density in nonequilibrium phase transitions, rather than the excitations in the corresponding Hermitian systems. The result shows that the adiabatic-impulse approximation, which is fundamental to the Kibble-Zurek mechanism, may be adapted to the parity-time symmetric non-Hermitian Landau-Zener models to examine the dynamics near the critical point. The most basic non-Hermitian two-level models with an exact solution exhibiting the Kibble-Zurek mechanism are presented. It would be interesting to extend this scenario to quantum many-body models, such as the quantum phase transition in the Ising model.