Bulk-edge correspondence in non-Hermitian systems & physics sensitive vs. insensitive to the boundary condition
Ken-Ichiro Imura
U. Tokyko

A non-Hermitian system with asymmetric or non-reciprocal type hopping (e.g., the Hatano-Nelson model) shows an extreme sensitivity to the choice of the boundary condition in its fundamental physical properties. Under the open boundary condition (OBC) it exhibits a skin effect, while the characteristic complex spectrum is unique to the periodic boundary condition (PBC). To think of the bulk and edge of the system is, on the other hand, indispensable for the concept of topological insulator, which in reality (at least in theory and in simulations) consists in changing the boundary condition. Here, we discuss outcomes and difficulties when the two concepts meet.