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Universal Generalized Brillouin Zone Theory I: Review of the Spectral Approach
Abstract
This series of papers aims to establish a universal generalized Brillouin zone (GBZ) theory for higher-dimensional non-Hermitian systems. As the starting point of this series, we emphasize a fundamental question: while the conventional one-dimensional (1D) GBZ condition, |βp| = |βp+1|, is well known to fail in two dimensions, how does this breakdown actually occur as a system gradually crosses over from 1D to 2D? Investigating this question reveals that the existing 1D GBZ theory itself remains incomplete. In this first paper, we therefore systematically review the 1D spectral approach and clarify where the underlying difficulties lie. Our work identifies the key challenges that motivate the wavefunction approach developed in Paper~II.
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BibTeX
@misc{xu2026universal,
title = {{Universal Generalized Brillouin Zone Theory I: Review of the Spectral Approach}},
author = {Zeqi xu and Jiangping Hu and Zhesen Yang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23523},
eprint = {2609.23523},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23523},
}
RIS
TY - UNPB
TI - Universal Generalized Brillouin Zone Theory I: Review of the Spectral Approach
AU - Zeqi xu
AU - Jiangping Hu
AU - Zhesen Yang
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.23523
UR - https://arxiv.org/abs/2609.23523
AB - This series of papers aims to establish a universal generalized Brillouin zone (GBZ) theory for higher-dimensional non-Hermitian systems. As the starting point of this series, we emphasize a fundamental question: while the conventional one-dimensional (1D) GBZ condition, |β_p| = |β_p+1|, is well known to fail in two dimensions, how does this breakdown actually occur as a system gradually crosses over from 1D to 2D? Investigating this question reveals that the existing 1D GBZ theory itself remains incomplete. In this first paper, we therefore systematically review the 1D spectral approach and clarify where the underlying difficulties lie. Our work identifies the key challenges that motivate the wavefunction approach developed in Paper~II.
ER -