Bulk-boundary correspondence in point-gap topological phases

The bulk-boundary correspondence (BBC) is a fundamental principle in Hermitian topological phases. It, however, has been known that the BBC may break down in non-Hermitian systems. The key is the difference between the bulk spectra under open boundary conditions (OBCs) and that under periodic boundary conditions (PBCs) due to the non-Hermitian skin effect. Since non-Hermitian Hamiltonians take the complex energy, we can define two types of topological phases, line-gap and point-gap topological phases. Many previous works have shown that the BBC becomes valid again for the line-gap topological phases if the bulk spectra under OBCs are treated properly. On the other hand, the BBC for the point-gap topological phases has remained unclear. Here, we clarify that the classification of bulk point-gap topological phases in OBCs can be different from those in PBCs. Moreover, we show that the BBC also exists for the point-gap topological phases by introducing real-space point-gap topological numbers defined under OBCs.

*This work was done while Takumi Bessho was at Yukawa Institute for Theoretical Physics.