Topological insulating phase for anti-Hermitian Hamiltonians

We study classification of anti-Hermitian topological insulators based on the discrete symmetries: time-reversal, particle-hole and chiral symmetries. Contrary to the most general form of non-Hermitian systems, bulk boundary correspondence can hold in anti-Hermitian topological systems. We map a topologically nontrivial Hermitian Hamiltonians into an anti-Hermitian system and we show that the standard table of topological insulators can be used for anti-Hermitian Hamiltonians. •We discuss that bulk boundary condition can be satisfied for anti-Hermitian topological insulators.•We show that the standard table of topological insulators can be used for anti-Hermitian systems.•We show that topological zero energy modes are available in the anti-Hermitian SHS model.