General theory for geometry-dependent non-Hermitian bands

Fuente: arXiv
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Main Authors: Wang, Chenyang, Pi, Jinghui, Liu, Qinxin, Li, Yaohua, Liu, Yong-Chun
Format: Preprint
Published: 2025
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_version_ 1866909890469953536
author Wang, Chenyang
Pi, Jinghui
Liu, Qinxin
Li, Yaohua
Liu, Yong-Chun
author_facet Wang, Chenyang
Pi, Jinghui
Liu, Qinxin
Li, Yaohua
Liu, Yong-Chun
contents In two- and higher-dimensional non-Hermitian lattices, systems can exhibit geometry-dependent bands, where the spectrum and eigenstates under open boundary conditions depend on the bulk geometry even in the thermodynamic limit. Although geometry-dependent bands are widely observed, the underlying mechanism for this phenomenon remains unclear. In this work, we address this problem by establishing a higher-dimensional non-Bloch band theory based on the concept of "strip generalized Brillouin zones" (SGBZs), which describe the asymptotic behavior of non-Hermitian bands when a lattice is extended sequentially along its linearly independent axes. Within this framework, we demonstrate that geometry-dependent bands arise from the incompatibility of SGBZs and, for the first time, derive a general criterion for the geometry dependence of non-Hermitian bands: non-zero area of the complex energy spectrum or the imaginary momentum spectrum. Our work opens an avenue for future studies on the interplay between geometric effects and non-Hermitian physics, such as non-Hermitian band topology.
format Preprint
id arxiv_https___arxiv_org_abs_2506_22743
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle General theory for geometry-dependent non-Hermitian bands
Wang, Chenyang
Pi, Jinghui
Liu, Qinxin
Li, Yaohua
Liu, Yong-Chun
Mesoscale and Nanoscale Physics
Quantum Gases
Mathematical Physics
Optics
Quantum Physics
In two- and higher-dimensional non-Hermitian lattices, systems can exhibit geometry-dependent bands, where the spectrum and eigenstates under open boundary conditions depend on the bulk geometry even in the thermodynamic limit. Although geometry-dependent bands are widely observed, the underlying mechanism for this phenomenon remains unclear. In this work, we address this problem by establishing a higher-dimensional non-Bloch band theory based on the concept of "strip generalized Brillouin zones" (SGBZs), which describe the asymptotic behavior of non-Hermitian bands when a lattice is extended sequentially along its linearly independent axes. Within this framework, we demonstrate that geometry-dependent bands arise from the incompatibility of SGBZs and, for the first time, derive a general criterion for the geometry dependence of non-Hermitian bands: non-zero area of the complex energy spectrum or the imaginary momentum spectrum. Our work opens an avenue for future studies on the interplay between geometric effects and non-Hermitian physics, such as non-Hermitian band topology.
title General theory for geometry-dependent non-Hermitian bands
topic Mesoscale and Nanoscale Physics
Quantum Gases
Mathematical Physics
Optics
Quantum Physics
url https://arxiv.org/abs/2506.22743