Dynamical Quantum Phase Transition in non-Hermitian Floquet Model

Abstract

Weanalyze the Dynamical Topological Quantum Phase transition (DTQPT), in dissipative and periodically driven XY and extended XY Model with induced gain and loss. In the non-hermitian Hamiltonian, of the system the imaginary term represents the interaction process with environment. We find three regions of the system by non-Hermitian gap of the time dependent non hermitian Hamiltonian, real energy gap enclosed by exceptional ring, pure imaginary gap and complex gap. We further identify these three regions by complex geometrical non adiabatic phase. In a region where eigen values of the time independent effective floquet non-Hermitian Hamiltonian, are real f loquet topological dynamical Quantum Phase transition (DQPT) occurs, where the real energy gap region is ferromagnetic region and other two are paramagnetic regions. We find out the range of driven frequency over which the DFDQPT occurs, by increasing the dissipation in the range of driven frequency shrink to single point.