Bulk-edge correspondence in 1D non-Hermitian systems

Recently, the role of the topology in non-Hermitian systems is attracting much attention. It is known fact is that the conventional bulk-edge correspondence breaks down in non-Hermitian systems if the Bloch wavevector k is set to be real. Here, to restore the bulk-edge correspondence, the non-Bloch factor β≡exp(ik), k∈C is introduced in the SSH model with the asymmetric hopping [1]. In this case, one can show the bulk-edge correspondence by defining the winding number by using β. However, it is not obvious how to systematically calculate β in general case. In this talk, we show how to calculate β in general 1D models for constructing the continuum bulk-bands. It is non-trivial because the states in the continuum bulk-bands do not extend over the bulk, unlike those in the Hermitian systems. We also discuss the bulk-edge correspondence in general cases by defining the generalized Brillouin zone in terms of β. [1] S.Yao, et al., Phys. Rev. Lett. 121, 086803 (2018)