An elementary rigorous proof of bulk-boundary correspondence in the generalized Su-Schrieffer-Heeger model. (English) Zbl 1448.81443
Summary: We generalize the Su-Schrieffer-Heeger (SSH) model with the inclusion of arbitrary long-range hopping amplitudes, providing a simple framework to investigate arbitrary adiabatic deformations that preserve the chiral symmetry upon the bulk energy bands with any arbitrary winding numbers. Using only elementary techniques of solving linear difference equations and applying Cauchy’s integral formula, we obtain a mathematically rigorous and physically transparent proof of the bulk-boundary correspondence for the generalized SSH model. The multiplicity of robust zero-energy edge modes is shown to be identical to the winding number. On the other hand, nonzero-energy edge modes, if any, are shown to be unstable under adiabatic deformations and not related to the topological invariant. Furthermore, under deformations of small spatial disorder, the zero-energy edge modes remain robust.
MSC:
| 81T45 | Topological field theories in quantum mechanics |
| 82D03 | Statistical mechanics in condensed matter (general) |
Keywords:
topological insulator; bulk-boundary correspondence; generalized Su-Schrieffer-Heeger model; edge states; winding numberReferences:
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