Non-Hermitian Bulk-Boundary Correspondence and Auxiliary Generalized Brillouin Zone Theory
Chinese Academy of Sciences · Kavli Institute for Theoretical Sciences · +4 more institutions
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…
Citation impact
- FWCI
- 37.27
- Percentile
- 100%
- References
- 66
Authors
4- ZYZhesen YangCorresponding
Chinese Academy of Sciences, Kavli Institute for Theoretical Sciences, Institute of Physics, University of Chinese Academy of Sciences
- KZKai Zhang
Chinese Academy of Sciences, Institute of Physics
- CFChen Fang
Chinese Academy of Sciences, Kavli Institute for Theoretical Sciences, Songshan Lake Materials Laboratory, Institute of Physics, University of Chinese Academy of Sciences
- JHJiangping Hu
Chinese Academy of Sciences, South Bay Interdisciplinary Science Center, Kavli Institute for Theoretical Sciences, Institute of Physics, University of Chinese Academy of Sciences
Topics & keywords
- Hermitian matrix
- Algebraic number
- Brillouin zone
- Eigenvalues and eigenvectors
- Hamiltonian (control theory)
- Physics
- Boundary value problem
- Analytic continuation