Matrix Factorization Approach to Bulk-Boundary Correspondence

We introduce a new approach based on matrix factorization to obtain a unified proof of the bulk-boundary correspondence for the five Altland–Zirnbauer symmetry classes, to which one-dimensional non-trivial topological systems belong. A rigorous definition of “stability” of zero modes is provided with the aim of bringing clarity to various claims in the literature about topological “protection” of boundary-localized states. We also explore how the topology of the bulk fermionic wavefunctions and the symmetries of a system influence the stability of the zero-energy modes.