Non-Hermitian Topological Invariants in Real Space
Abstract
The topology of non-Hermitian systems is drastically shaped by the non-Hermitian skin effect, which leads to the generalized bulk-boundary correspondence and non-Bloch band theory. The essential part in formulations of bulk-boundary correspondence is a general and computable definition of topological invariants. In this Letter, we introduce a construction of non-Hermitian topological invariants based directly on real-space wave functions, which provides a general and straightforward approach for determining non-Hermitian topology. As an illustration, we apply this formulation to several representative models of non-Hermitian systems, efficiently obtaining their topological invariants in the presence of non-Hermitian skin effect. Our formulation also provides a dual picture of the non-Bloch band theory based on the generalized Brillouin zone, offering a unique perspective of bulk-boundary correspondence.
- Publication:
-
Physical Review Letters
- Pub Date:
- December 2019
- DOI:
- 10.1103/PhysRevLett.123.246801
- arXiv:
- arXiv:1905.02211
- Bibcode:
- 2019PhRvL.123x6801S
- Keywords:
-
- Condensed Matter - Mesoscale and Nanoscale Physics;
- Condensed Matter - Quantum Gases;
- Condensed Matter - Strongly Correlated Electrons;
- Physics - Optics
- E-Print:
- 6 pages, 3 figures