Dissipative Floquet Dynamical Quantum Phase Transition

Abstract

Non-Hermitian Hamiltonians provide a simple picture for inspecting dissipative systems with natural or induced gain and loss. We investigate the Floquet dynamical phase transition in the dissipative periodically time driven XY and extended XY models, where the imaginary terms represent the physical gain and loss during the interacting processes with the environment. The time-independent effective Floquet non-Hermitian Hamiltonians disclose three regions by analyzing the non-Hermitian gap: pure real gap (real eigenvalues), pure imaginary gap, and complex gap. We show that each region of the system can be distinguished by the complex geometrical non-adiabatic phase. We have discovered that in the presence of dissipation, the Floquet dynamical phase transitions (FDPTs) still exist in the region where the time-independent effective Floquet non-Hermitian Hamiltonians reveal real eigenvalues. Opposed to expectations based on earlier works on quenched systems, our findings show that the existence of the non-Hermitian topological phase is not an essential condition for dissipative FDPTs (DFDPTs). We also demonstrate the range of driven frequency, over which the DFDPTs occur, narrows down by increasing the dissipation coupling and shrinks to a single point at the critical value of dissipation. Moreover, quantization and jumps of the dynamical geometric phase reveals the topological characteristic feature of DFDPTs in the real gap region where confined to exceptional points.

Out-of-time-order correlations and Floquet dynamical quantum phase transition

“…Recently, a new research area of quantum phase transition has been investigated in nonequilibrium quantum systems, called dynamical quantum phase transitions (DQPTs) as a counterpart of equilibrium thermal phase transitions [75,76]. DQPT represents a phase transitions between dynamically emerging quantum phases, that occurs during the nonequilibrium coherent quantum time evolution under quenching [76][77][78][79][80] or time-periodic modulation of Hamiltonian [81][82][83][84][85][86][87]. In DQPT the real time acts as a control parameter analogous to temperature in conventional equilibrium phase transitions.…”

“…The eigenstates and eigenvalues of the Hamiltonian Eq. ( 11) are obtained by solving the time dependent Schrödinger equation [81][82][83]86] (see Appendix B).…”