Hybrid scaling properties of localization transition in a non-Hermitian disorder Aubry-André model
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| Format: | Preprint |
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2024
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| _version_ | 1866929598001840128 |
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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 |
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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 |