Topological insulator-superconductor phase transition in a non-Hermitian spin chain

Non-Hermitian systems can host nontrivial topological phases with the topological characterization distinct from Hermitian systems. Here we consider a 1D XY spin model with non-Hermitian out-of-plane magnetic field, which is periodically modulated. For isotropic XY interaction, the system corresponds to a topological insulator (TI) with pseudo-anti-Hermiticity, which supports edge states characterized by the quantized Zak phase. The anisotropy of XY interaction gives raise to superconducting paring, and the system experiences a transition from TI to topological superconducting (TSC) as the anisotropy increases. The transition point, where the system undergoes a band touch at E=0, can be tuned by the modulation phases and amplitudes of the non-Hermitian field. The TSC phase supports Majorana edge modes, protected by the chiral symmetry. The model can be experimentally simulated with trapped ions. Our work provides a method to investigate the interplay between non-Hermiticity and superconducting interaction and paves the way for exploring various topological insulators and superconductors in non-Hermitian systems.