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 nonadiabatic 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.
Highlights
Non-Hermitian Hamiltonians have recently attracted a lot of attention in the physics community across a wide range of fields, owing to their experimental feasibility [1–18] and theoretical richness [19–28]
We show that the phase diagram of the system divided into three regions with pure real gap where confined to exceptional points, pure imaginary gap, and complex gap
We have investigated the dissipative Floquet dynamical phase transition in the periodically time-driven XY and extended XY models in the presence of the imaginary terms, which represent the physical gain and loss during the interacting processes with the environment
Summary
Non-Hermitian Hamiltonians have recently attracted a lot of attention in the physics community across a wide range of fields, owing to their experimental feasibility [1–18] and theoretical richness [19–28]. We probe the phase diagram of the time-independent effective Floquet non-Hermitian Hamiltonians by analyzing the energy gap of the systems analytically. The region with real energy gap, where the DFDPTs occur, is topologically nontrivial in the time-independent effective Floquet non-Hermitian XY Hamiltonian. Different from results obtained for the quenched case [64], existence of the non-Hermitian topologically nontrivial phase is not a necessary condition for appearance of the DFDPTs. We have shown that, the DFDPTs driven frequency range narrows down by increasing the dissipation coupling and shrinks to a single point at critical value of dissipation. We have found that adding the dissipation (imaginary term) to the Hermitian Hamiltonians affects those bounds of the driven frequency range which correspond to the critical (gap closing) points of the time-independent effective Floquet Hermitian Hamiltonians
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