Complex Band Structure and localisation transition for tridiagonal non-Hermitian k-Toeplitz operators with defects

Yannick De Bruijn; Erik Orvehed Hiltunen

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arXiv · 2505.23610

Complex Band Structure and localisation transition for tridiagonal non-Hermitian k-Toeplitz operators with defects

Yannick De Bruijn·Erik Orvehed Hiltunen

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Abstract

Using the Bloch-Floquet theory, we propose an innovative technique to obtain the eigenvectors of tridiagonal k-Toeplitz operators. This method offers a more extensive and quantitative basis for describing localised eigenvectors beyond the non-trivial winding zone, yielding sharp decay bounds. The validity of our results is confirmed numerically in one-dimensional resonator chains, showcasing non-Hermitian skin localisation, bulk localisation, and tunnelling effects. We conclude the paper by analysing non-Hermitian tight binding Hamiltonians, illustrating the broad applicability of the complex band structure.

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Yannick De Bruijn, Erik Orvehed Hiltunen. 2025-05-29. Complex Band Structure and localisation transition for tridiagonal non-Hermitian k-Toeplitz operators with defects. https://arxiv.org/abs/2505.23610

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