TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.7.1.003
TI  - A linear algebra-based approach to understanding the relation between the winding number and zero-energy edge states
PY  - 2024/01/30
UR  - https://scipost.org/SciPostPhysCore.7.1.003
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 7
IS  - 1
SP  - 003
A1  - Lee, Chen-Shen
AB  - The one-to-one relation between the winding number and the number of robust zero-energy edge states, known as bulk-boundary correspondence, is a celebrated feature of 1$d$ systems with chiral symmetry. Although this property can be explained by the K-theory, the underlying mechanism remains elusive. Here, we demonstrate that, even without resorting to advanced mathematical techniques, one can prove this correspondence and clearly illustrate the mechanism using only Cauchy's integral and elementary algebra. Furthermore, our approach to proving bulk-boundary correspondence also provides clear insights into a kind of system that doesn't respect chiral symmetry but can have robust left or right zero-energy edge states. In such systems, one can still assign the winding number to characterize these zero-energy edge states.
ER  -

@Article{10.21468/SciPostPhysCore.7.1.003,
	title={{A linear algebra-based approach to understanding the relation between the winding number and zero-energy edge states}},
	author={Chen-Shen Lee},
	journal={SciPost Phys. Core},
	volume={7},
	pages={003},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.7.1.003},
	url={https://scipost.org/10.21468/SciPostPhysCore.7.1.003},
}