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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/2412.07800 |
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| _version_ | 1866916679778304000 |
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| author | Xu, Mingtao Yi, Wei Cai, De-Huan |
| author_facet | Xu, Mingtao Yi, Wei Cai, De-Huan |
| contents | In quantum dynamics, the Loschmidt amplitude is analogous to the partition function in the canonical ensemble. Zeros in the partition function indicate a phase transition, while the presence of zeros in the Loschmidt amplitude indicates a dynamical quantum phase transition. Based on the classical-quantum correspondence, we demonstrate that the partition function of a classical Ising model is equivalent to the Loschmidt amplitude in non-Hermitian dynamics, thereby mapping an Ising model with variable system size to the non-Hermitian dynamics. It follows that the Yang-Lee zeros and the Yang-Lee edge singularity of the classical Ising model correspond to the critical times of the dynamic quantum phase transitions and the exceptional point of the non-Hermitian Hamiltonian, respectively. Our work reveals an inner connection between Yang-Lee zeros and non-Hermitian dynamics, offering a dynamic characterization of the former. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07800 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characterizing the Yang-Lee zeros of the classical Ising model through dynamic quantum phase transitions Xu, Mingtao Yi, Wei Cai, De-Huan Quantum Physics Quantum Gases Statistical Mechanics In quantum dynamics, the Loschmidt amplitude is analogous to the partition function in the canonical ensemble. Zeros in the partition function indicate a phase transition, while the presence of zeros in the Loschmidt amplitude indicates a dynamical quantum phase transition. Based on the classical-quantum correspondence, we demonstrate that the partition function of a classical Ising model is equivalent to the Loschmidt amplitude in non-Hermitian dynamics, thereby mapping an Ising model with variable system size to the non-Hermitian dynamics. It follows that the Yang-Lee zeros and the Yang-Lee edge singularity of the classical Ising model correspond to the critical times of the dynamic quantum phase transitions and the exceptional point of the non-Hermitian Hamiltonian, respectively. Our work reveals an inner connection between Yang-Lee zeros and non-Hermitian dynamics, offering a dynamic characterization of the former. |
| title | Characterizing the Yang-Lee zeros of the classical Ising model through dynamic quantum phase transitions |
| topic | Quantum Physics Quantum Gases Statistical Mechanics |
| url | https://arxiv.org/abs/2412.07800 |