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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.16704 |
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| _version_ | 1866909511042727936 |
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| author | Zeng, Chen-Chang Cai, Zhen Wang, Guang-Heng Sun, Gaoyong |
| author_facet | Zeng, Chen-Chang Cai, Zhen Wang, Guang-Heng Sun, Gaoyong |
| contents | We study the critical behaviors of the ground and first excited states in the one-dimensional nonreciprocal Aubry-Andr{é}-Harper model using both the self-normal and biorthogonal fidelity susceptibilities. We demonstrate that fidelity susceptibility serves as a probe for the phase transition in the nonreciprocal AAH model. For ground states, characterized by real eigenenergies across the entire regime, both fidelity susceptibilities near the critical points scale as $N^{2}$, akin to the Hermitian AAH model. However, for the first-excited states, the fidelity susceptibilities exhibit distinct scaling laws, contingent upon whether the lattice consists of even or odd sites. For even lattices, both the self-normal and biorthogonal fidelity susceptibilities near the critical points continue to scale as $N^{2}$. In contrast, for odd lattices, the biorthogonal fidelity susceptibilities diverge, while the self-normal fidelity susceptibilities exhibit linear behavior, indicating a novel scaling law. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16704 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fidelity and criticality in the nonreciprocal Aubry-Andr{é}-Harper model Zeng, Chen-Chang Cai, Zhen Wang, Guang-Heng Sun, Gaoyong Disordered Systems and Neural Networks We study the critical behaviors of the ground and first excited states in the one-dimensional nonreciprocal Aubry-Andr{é}-Harper model using both the self-normal and biorthogonal fidelity susceptibilities. We demonstrate that fidelity susceptibility serves as a probe for the phase transition in the nonreciprocal AAH model. For ground states, characterized by real eigenenergies across the entire regime, both fidelity susceptibilities near the critical points scale as $N^{2}$, akin to the Hermitian AAH model. However, for the first-excited states, the fidelity susceptibilities exhibit distinct scaling laws, contingent upon whether the lattice consists of even or odd sites. For even lattices, both the self-normal and biorthogonal fidelity susceptibilities near the critical points continue to scale as $N^{2}$. In contrast, for odd lattices, the biorthogonal fidelity susceptibilities diverge, while the self-normal fidelity susceptibilities exhibit linear behavior, indicating a novel scaling law. |
| title | Fidelity and criticality in the nonreciprocal Aubry-Andr{é}-Harper model |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2404.16704 |