Universal spectral moment theorem and its applications in non-Hermitian systems
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915127316447232 |
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| author | Cheng, Nan Shu, Chang Zhang, Kai Mao, Xiaoming Sun, Kai |
| author_facet | Cheng, Nan Shu, Chang Zhang, Kai Mao, Xiaoming Sun, Kai |
| contents | The high sensitivity of the spectrum and wavefunctions to boundary conditions, termed the non-Hermitian skin effect, represents a fundamental aspect of non-Hermitian systems. While it endows non-Hermitian systems with unprecedented physical properties, it presents notable obstacles in grasping universal properties that are robust against microscopic details and boundary conditions. In this Letter, we introduce a pivotal theorem: in the thermodynamic limit, for any non-Hermitian systems with finite-range interactions, all spectral moments are invariant quantities, independent of boundary conditions, posing strong constraints on the spectrum. Utilizing this invariance, we propose a new criterion for bulk dynamical phases based on experimentally observable features and applicable to any dimensions and any boundary conditions. Based on this criterion, we define the bulk dispersive-to-proliferative phase transition, which is distinct from the real-to-complex spectral transition and contrary to traditional expectations. We verify these findings in 1D and 2D lattice models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01583 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universal spectral moment theorem and its applications in non-Hermitian systems Cheng, Nan Shu, Chang Zhang, Kai Mao, Xiaoming Sun, Kai Mesoscale and Nanoscale Physics Quantum Gases Optics The high sensitivity of the spectrum and wavefunctions to boundary conditions, termed the non-Hermitian skin effect, represents a fundamental aspect of non-Hermitian systems. While it endows non-Hermitian systems with unprecedented physical properties, it presents notable obstacles in grasping universal properties that are robust against microscopic details and boundary conditions. In this Letter, we introduce a pivotal theorem: in the thermodynamic limit, for any non-Hermitian systems with finite-range interactions, all spectral moments are invariant quantities, independent of boundary conditions, posing strong constraints on the spectrum. Utilizing this invariance, we propose a new criterion for bulk dynamical phases based on experimentally observable features and applicable to any dimensions and any boundary conditions. Based on this criterion, we define the bulk dispersive-to-proliferative phase transition, which is distinct from the real-to-complex spectral transition and contrary to traditional expectations. We verify these findings in 1D and 2D lattice models. |
| title | Universal spectral moment theorem and its applications in non-Hermitian systems |
| topic | Mesoscale and Nanoscale Physics Quantum Gases Optics |
| url | https://arxiv.org/abs/2403.01583 |