Many-body phase transitions in a non-Hermitian Ising chain
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866916351118934016 |
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| author | Lu, Chao-Ze Deng, Xiaolong Kou, Su-Peng Sun, Gaoyong |
| author_facet | Lu, Chao-Ze Deng, Xiaolong Kou, Su-Peng Sun, Gaoyong |
| contents | We study many-body phase transitions in a one-dimensional ferromagnetic transversed field Ising model with an imaginary field and show that the system exhibits three phase transitions: one second-order phase transition and two $\mathcal{PT}$ phase transitions. The second-order phase transition occurring in the ground state is investigated via biorthogonal and self-normal entanglement entropy, for which we develop an approach to perform finite-size scaling theory to extract the central charge for small systems. Compared with the second-order phase transition, the first $\mathcal{PT}$ transition is characterized by the appearance of an exceptional point in the full energy spectrum, while the second $\mathcal{PT}$ transition only occurs in specific excited states. Furthermore, we interestingly show that both of exceptional points are second-order in terms of scalings of imaginary parts of the energy. This work provides an exact solution for many-body phase transitions in non-Hermitian systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_11251 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Many-body phase transitions in a non-Hermitian Ising chain Lu, Chao-Ze Deng, Xiaolong Kou, Su-Peng Sun, Gaoyong Strongly Correlated Electrons Quantum Physics We study many-body phase transitions in a one-dimensional ferromagnetic transversed field Ising model with an imaginary field and show that the system exhibits three phase transitions: one second-order phase transition and two $\mathcal{PT}$ phase transitions. The second-order phase transition occurring in the ground state is investigated via biorthogonal and self-normal entanglement entropy, for which we develop an approach to perform finite-size scaling theory to extract the central charge for small systems. Compared with the second-order phase transition, the first $\mathcal{PT}$ transition is characterized by the appearance of an exceptional point in the full energy spectrum, while the second $\mathcal{PT}$ transition only occurs in specific excited states. Furthermore, we interestingly show that both of exceptional points are second-order in terms of scalings of imaginary parts of the energy. This work provides an exact solution for many-body phase transitions in non-Hermitian systems. |
| title | Many-body phase transitions in a non-Hermitian Ising chain |
| topic | Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2311.11251 |