Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory
Abstract
We provide a systematic and self-consistent method to calculate the generalized Brillouin Zone (GBZ) analytically in one dimensional non-Hermitian systems, which helps us to understand the non-Hermitian bulk-boundary correspondence. In general, a n-band non-Hermitian Hamiltonian is constituted by n distinct sub-GBZs, each of which is a piecewise analytic closed loop. Based on the concept of resultant, we can show that all the analytic properties of the GBZ can be characterized by an algebraic equation, the solution of which in the complex plane is dubbed as auxiliary GBZ (aGBZ). We also provide a systematic method to obtain the GBZ from aGBZ. Two physical applications are also discussed. Our method provides an analytic approach to the spectral problem of open boundary non-Hermitian systems in the thermodynamic limit.
Keywords
Cite
@article{arxiv.1912.05499,
title = {Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory},
author = {Zhesen Yang and Kai Zhang and Chen Fang and Jiangping Hu},
journal= {arXiv preprint arXiv:1912.05499},
year = {2020}
}
Comments
6+16 pages, 5+5 figures. To appear in Physical Review Letters