Hybrid scaling properties of localization transition in a non-Hermitian disorder Aubry-André model

Fuente: arXiv
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Main Authors: Sun, Yue-Mei, Wang, Xin-Yu, Zhai, Liang-Jun
Format: Preprint
Published: 2024
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author Sun, Yue-Mei
Wang, Xin-Yu
Zhai, Liang-Jun
author_facet Sun, Yue-Mei
Wang, Xin-Yu
Zhai, Liang-Jun
contents In this paper, we study the critical behaviors in the non-Hermitian disorder Aubry-André (DAA) model, and we assume the non-Hermiticity is introduced by nonreciprocal hopping. We employ the localization length $ξ$, the inverse participation ratio ($\rm IPR$), and the energy gap $ΔE$ as the characteristic quantities to describe the critical properties of the localization transition. By performing scaling analysis, the critical exponents of the non-Hermitian Anderson model and the non-Hermitian DAA model are obtained, and these critical exponents are different from their Hermitian counterparts, indicating that the Hermitian and non-Hermitian Anderson and DAA models belong to different universality classes. The critical exponents of the non-Hermitian DAA model are remarkably different from both the pure non-Hermitian AA model and the non-Hermitian Anderson model, showing that disorder is an independent relevant direction at the non-Hermitian AA model critical point. We further propose a hybrid scaling law to describe the critical behavior in the overlapping critical region constituted by the critical regions of the non-Hermitian DAA model and the non-Hermitian Anderson localization.
format Preprint
id arxiv_https___arxiv_org_abs_2405_15220
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Hybrid scaling properties of localization transition in a non-Hermitian disorder Aubry-André model
Sun, Yue-Mei
Wang, Xin-Yu
Zhai, Liang-Jun
Disordered Systems and Neural Networks
In this paper, we study the critical behaviors in the non-Hermitian disorder Aubry-André (DAA) model, and we assume the non-Hermiticity is introduced by nonreciprocal hopping. We employ the localization length $ξ$, the inverse participation ratio ($\rm IPR$), and the energy gap $ΔE$ as the characteristic quantities to describe the critical properties of the localization transition. By performing scaling analysis, the critical exponents of the non-Hermitian Anderson model and the non-Hermitian DAA model are obtained, and these critical exponents are different from their Hermitian counterparts, indicating that the Hermitian and non-Hermitian Anderson and DAA models belong to different universality classes. The critical exponents of the non-Hermitian DAA model are remarkably different from both the pure non-Hermitian AA model and the non-Hermitian Anderson model, showing that disorder is an independent relevant direction at the non-Hermitian AA model critical point. We further propose a hybrid scaling law to describe the critical behavior in the overlapping critical region constituted by the critical regions of the non-Hermitian DAA model and the non-Hermitian Anderson localization.
title Hybrid scaling properties of localization transition in a non-Hermitian disorder Aubry-André model
topic Disordered Systems and Neural Networks
url https://arxiv.org/abs/2405.15220