Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter pp 159-190 | Cite as

# Mathematical Foundations to the Generalized Bloch Theorem

## Abstract

This chapter presents the mathematical results that were used in establishing the generalized Bloch theorem in Chap. 2. We work directly with possibly non-Hermitian block-Toeplitz matrices, so as to keep the formalism as general as possible. There are two main takeaways as part of the proof of the generalized Bloch theorem: First, a simple yet effective separation of the time-independent Schrödinger equation into bulk and boundary equations is what really allows us to capture the exact interplay between the bulk and the BCs; second, the Smith normal form of matrix polynomials emerges as a natural tool in the treatment of systems with boundary.

## Keywords

Non-Hermitian banded block-Toeplitz matrices Smith normal form Bulk-boundary correspondence Lattice models## References

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