Exact mobility line and mobility ring in the complex energy plane of a flat band lattice with a non-Hermitian quasiperiodic potential

Fuente: arXiv
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Main Authors: Pang, Guang-Xin, Li, Zhi, Li, Shan-Zhong, Zhang, Yan-Yang, Liu, Jun-Feng, Zhang, Yi-Cai
Format: Preprint
Published: 2025
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_version_ 1866909645608583168
author Pang, Guang-Xin
Li, Zhi
Li, Shan-Zhong
Zhang, Yan-Yang
Liu, Jun-Feng
Zhang, Yi-Cai
author_facet Pang, Guang-Xin
Li, Zhi
Li, Shan-Zhong
Zhang, Yan-Yang
Liu, Jun-Feng
Zhang, Yi-Cai
contents In this study, we investigate the problem of Anderson localization in a one-dimensional flat band lattice with a non-Hermitian quasiperiodic on-site potential. First of all, we discuss the influences of non-Hermitian potentials on the existence of critical states. Our findings show that, unlike in Hermitian cases, the non-Hermiticity of the potential leads to the disappearance of critical states and critical regions. Furthermore, we are able to accurately determine the Lyapunov exponents and the mobility edges. Our results reveal that the mobility edges form mobility lines and mobility rings in the complex energy plane. Within the mobility rings, the eigenstates are extended, while the localized states are located outside the mobility rings. For mobility line cases, only when the eigenenergies lie on the mobility lines, their corresponding eigenstates are extended states.Finally, as the energy approaches the mobility edges, we observe that, differently from Hermitian cases, here the critical index of the localization length is not a constant, but rather varies depending on the positions of the mobility edges.
format Preprint
id arxiv_https___arxiv_org_abs_2504_08760
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Exact mobility line and mobility ring in the complex energy plane of a flat band lattice with a non-Hermitian quasiperiodic potential
Pang, Guang-Xin
Li, Zhi
Li, Shan-Zhong
Zhang, Yan-Yang
Liu, Jun-Feng
Zhang, Yi-Cai
Disordered Systems and Neural Networks
Quantum Gases
In this study, we investigate the problem of Anderson localization in a one-dimensional flat band lattice with a non-Hermitian quasiperiodic on-site potential. First of all, we discuss the influences of non-Hermitian potentials on the existence of critical states. Our findings show that, unlike in Hermitian cases, the non-Hermiticity of the potential leads to the disappearance of critical states and critical regions. Furthermore, we are able to accurately determine the Lyapunov exponents and the mobility edges. Our results reveal that the mobility edges form mobility lines and mobility rings in the complex energy plane. Within the mobility rings, the eigenstates are extended, while the localized states are located outside the mobility rings. For mobility line cases, only when the eigenenergies lie on the mobility lines, their corresponding eigenstates are extended states.Finally, as the energy approaches the mobility edges, we observe that, differently from Hermitian cases, here the critical index of the localization length is not a constant, but rather varies depending on the positions of the mobility edges.
title Exact mobility line and mobility ring in the complex energy plane of a flat band lattice with a non-Hermitian quasiperiodic potential
topic Disordered Systems and Neural Networks
Quantum Gases
url https://arxiv.org/abs/2504.08760