Transfer matrix analysis of non-hermitian Hamiltonians: asymptotic spectra and topological eigenvalues
Mathematical Physics
2024-10-08 v2 Disordered Systems and Neural Networks
math.MP
Abstract
Transfer matrix techniques are used to provide a new proof of Widom's results on the asymptotic spectral theory of finite block Toeplitz matrices. Furthermore, a rigorous treatment of the skin effect, spectral outliers, the generalized Brillouin zone and the bulk-boundary correspondence in such systems is given. This covers chiral Hamiltonians with topological eigenvalues close to zero, but no line-gap.
Keywords
Cite
@article{arxiv.2403.18942,
title = {Transfer matrix analysis of non-hermitian Hamiltonians: asymptotic spectra and topological eigenvalues},
author = {Lars Koekenbier and Hermann Schulz-Baldes},
journal= {arXiv preprint arXiv:2403.18942},
year = {2024}
}
Comments
version published in Journal of Spectral Theory; numerous misprints corrected and several minor improvement implemented