Non-Hermitian bulk-boundary correspondence and skin effect

Recently, the conventional Bulk-boundary correspondence (BBC) is challenged in some non-Hermitian systems, e.g. the spectrum between open and periodic boundary conditions can be totally distinct [1]. In this talk, I will reveal the two-fold meaning of the non-Hermitian BBC [2]. On the one hand, the conventional boundary state is related to the wavefunction topology of the so-called generalized Brillouin zone (GBZ) Hamiltonian [1]; On the other hand, the non-Hermitian skin mode is related to the energy-spectra topology of the Bloch Hamiltonian [3]. An analytic method is introduced to calculate the GBZ exactly [2]. Finally, we will briefly discuss how to realize the non-Hermitian skin effect in condensed matter systems [4].  [1] Shunyu Yao and Zhong Wang, Phys. Rev. Lett. 121, 086803 (2018).[2] Zhesen Yang*, Kai Zhang*, Chen Fang, and Jiangping Hu, arXiv:1912.05499 (To appear in PRL)[3] Kai Zhang*, Zhesen Yang*, and Chen Fang, Phys. Rev. Lett. 125, 126402 (2020) [4] Yifei Yi, and Zhesen Yang†, Phys. Rev. Lett. 125, 186802 (2020)