English

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