Unified one-parameter scaling function for Anderson localization transitions in non-reciprocal non-Hermitian systems
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909215968198656 |
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| author | Wang, C. He, Wenxue Wang, X. R. Ren, Hechen |
| author_facet | Wang, C. He, Wenxue Wang, X. R. Ren, Hechen |
| contents | By using dimensionless conductances as scaling variables, the conventional one-parameter scaling theory of localization fails for non-reciprocal non-Hermitian systems such as the Hanato-Nelson model. Here, we propose a one-parameter scaling function using the participation ratio as the scaling variable. Employing a highly accurate numerical procedure based on exact diagonalization, we demonstrate that this one-parameter scaling function can describe Anderson localization transitions of non-reciprocal non-Hermitian systems in one and two dimensions of symmetry classes AI and A. The critical exponents of correlation lengths depend on symmetries and dimensionality only, a typical feature of universality. Moreover, we derive a complex-gap equation based on the self-consistent Born approximation that can determine the disorder at which the point gap closes. The obtained disorders match perfectly the critical disorders of Anderson localization transitions from the one-parameter scaling function. Finally, we show that the one-parameter scaling function is also valid for Anderson localization transitions in reciprocal non-Hermitian systems such as two-dimensional class AII$^\dagger$ and can, thus, serve as a unified scaling function for disordered non-Hermitian systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01984 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unified one-parameter scaling function for Anderson localization transitions in non-reciprocal non-Hermitian systems Wang, C. He, Wenxue Wang, X. R. Ren, Hechen Disordered Systems and Neural Networks By using dimensionless conductances as scaling variables, the conventional one-parameter scaling theory of localization fails for non-reciprocal non-Hermitian systems such as the Hanato-Nelson model. Here, we propose a one-parameter scaling function using the participation ratio as the scaling variable. Employing a highly accurate numerical procedure based on exact diagonalization, we demonstrate that this one-parameter scaling function can describe Anderson localization transitions of non-reciprocal non-Hermitian systems in one and two dimensions of symmetry classes AI and A. The critical exponents of correlation lengths depend on symmetries and dimensionality only, a typical feature of universality. Moreover, we derive a complex-gap equation based on the self-consistent Born approximation that can determine the disorder at which the point gap closes. The obtained disorders match perfectly the critical disorders of Anderson localization transitions from the one-parameter scaling function. Finally, we show that the one-parameter scaling function is also valid for Anderson localization transitions in reciprocal non-Hermitian systems such as two-dimensional class AII$^\dagger$ and can, thus, serve as a unified scaling function for disordered non-Hermitian systems. |
| title | Unified one-parameter scaling function for Anderson localization transitions in non-reciprocal non-Hermitian systems |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2406.01984 |