Driven nonhermitian transverse field 1D Ising model: topological edge modes and entanglement scaling

We study driven nonhermitian transverse field 1D Ising model (complex magnetic field and interactions). We find a mapping between the steady states of this model and the eingenstate order of the corresponding unitary problem, enriched by the complex character of parameters. When boundary conditions are open, the phases are associated with the presence or absence of Majorana modes, which show remarkable robustness to dissipation inherent in the model. We also establish the correspondence between the scaling behavior of entanglement entropy and the character of the complex quasiparticle spectrum.