Dynamical phase transition in n-cluster spin model

In this paper we consider a spin chain with cluster interaction which is under the transverse magnetic field and study its dynamical behavior as the magnetic field changes suddenly. Such a system, has exact solution by means of Jordan-Wigner transformations. We show that if the magnetic field changes in such a way that its initial and finial value be in two different equilibrium phase, then rate function of return probability diverges periodically in time which, this divergence in time, is called dynamical phase transition. If the quench has been done within the same phase, dynamical phase transition doesn’t happen. Furthermore, we have shown that Fisher zeros lines cross the imaginary axes when the dynamical phase transition occurs.