Topological metal-insulator transitions in one-dimensional non-Hermitian quasicrystals: beyond PT-symmetry
Abstract
One-dimensional non-Hermitian quasicrystals with parity and time-reversal (PT) symmetry can simultaneously exhibit localization-delocalization transition, topological phase transition, and PT-symmetry-breaking transition. This motivates us to investigate how the absence of PT symmetry impacts topological metal-insulator transitions in non-Hermitian quasicrystals. We propose a non-Hermitian quasiperiodic model that generally does not preserve PT-symmetry but, in most parameter regions, hosts a generic triple-transition scenario encompassing localization, topological, and degeneracy-breaking transitions. These transitions can be understood within the dual momentum-space representation featuring asymmetric couplings. Specifically, the localization boundary is obtained from the dual momentum-space representation by comparing the Lyapunov exponent, or inverse localization length, of the reciprocal Aubry-André model with the nonreciprocal hopping-asymmetry ratio of the dual lattice. The accompanying topological transition is characterized by a point-gap winding number defined with respect to a reference energy inside the complex spectral gap, whereas the degeneracy-breaking transition is understood from the loss of the reciprocal n↔ −n spectral symmetry. The system also exhibits a localization-delocalization transition analogous to that in the Hermitian case, which occurs without accompanying topological or degeneracy-breaking transitions. Our work extends the topological metal-insulator transitions previously studied in PT-symmetric systems to a more general class of non-Hermitian setting, and further reveals that non-Hermitian systems can host distinct types of localization behavior.
Versions
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BibTeX
@misc{zhang2026topological,
title = {{Topological metal-insulator transitions in one-dimensional non-Hermitian quasicrystals: beyond PT-symmetry}},
author = {Guangjie Zhang and Bing Shao and Longwen Zhou and Jiangbin Gong and Weiwei Zhu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2605.25072},
eprint = {2605.25072},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.25072},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Topological metal-insulator transitions in one-dimensional non-Hermitian quasicrystals: beyond PT-symmetry
AU - Guangjie Zhang
AU - Bing Shao
AU - Longwen Zhou
AU - Jiangbin Gong
AU - Weiwei Zhu
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2605.25072
UR - https://arxiv.org/abs/2605.25072
AB - One-dimensional non-Hermitian quasicrystals with parity and time-reversal (PT) symmetry can simultaneously exhibit localization-delocalization transition, topological phase transition, and PT-symmetry-breaking transition. This motivates us to investigate how the absence of PT symmetry impacts topological metal-insulator transitions in non-Hermitian quasicrystals. We propose a non-Hermitian quasiperiodic model that generally does not preserve PT-symmetry but, in most parameter regions, hosts a generic triple-transition scenario encompassing localization, topological, and degeneracy-breaking transitions. These transitions can be understood within the dual momentum-space representation featuring asymmetric couplings. Specifically, the localization boundary is obtained from the dual momentum-space representation by comparing the Lyapunov exponent, or inverse localization length, of the reciprocal Aubry-André model with the nonreciprocal hopping-asymmetry ratio of the dual lattice. The accompanying topological transition is characterized by a point-gap winding number defined with respect to a reference energy inside the complex spectral gap, whereas the degeneracy-breaking transition is understood from the loss of the reciprocal n↔ −n spectral symmetry. The system also exhibits a localization-delocalization transition analogous to that in the Hermitian case, which occurs without accompanying topological or degeneracy-breaking transitions. Our work extends the topological metal-insulator transitions previously studied in PT-symmetric systems to a more general class of non-Hermitian setting, and further reveals that non-Hermitian systems can host distinct types of localization behavior.
ER -