Adiabatic Transformations in Dissipative and Non-Hermitian Phase Transitions
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912246198697984 |
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| author | Orlov, Pavel Shlyapnikov, Georgy V. Kurlov, Denis V. |
| author_facet | Orlov, Pavel Shlyapnikov, Georgy V. Kurlov, Denis V. |
| contents | The quantum geometric tensor has established itself as a general framework for the analysis and detection of equilibrium phase transitions in isolated quantum systems. We propose a novel generalization of the quantum geometric tensor, which offers a universal approach to studying phase transitions in non-Hermitian quantum systems. Our generalization is based on the concept of the generator of adiabatic transformations and can be applied to systems described by either a Liouvillian superoperator or by an effective non-Hermitian Hamiltonian. We illustrate the proposed method by analyzing the non-Hermitian Su-Schrieffer-Heeger model and a generic quasi-free dissipative fermionic system with a quadratic Liouvillian. Our findings reveal that this method effectively identifies phase transitions across all examined models, providing a universal tool for investigating general non-Hermitian systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12337 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Adiabatic Transformations in Dissipative and Non-Hermitian Phase Transitions Orlov, Pavel Shlyapnikov, Georgy V. Kurlov, Denis V. Quantum Physics Statistical Mechanics The quantum geometric tensor has established itself as a general framework for the analysis and detection of equilibrium phase transitions in isolated quantum systems. We propose a novel generalization of the quantum geometric tensor, which offers a universal approach to studying phase transitions in non-Hermitian quantum systems. Our generalization is based on the concept of the generator of adiabatic transformations and can be applied to systems described by either a Liouvillian superoperator or by an effective non-Hermitian Hamiltonian. We illustrate the proposed method by analyzing the non-Hermitian Su-Schrieffer-Heeger model and a generic quasi-free dissipative fermionic system with a quadratic Liouvillian. Our findings reveal that this method effectively identifies phase transitions across all examined models, providing a universal tool for investigating general non-Hermitian systems. |
| title | Adiabatic Transformations in Dissipative and Non-Hermitian Phase Transitions |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2404.12337 |