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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/2411.06305 |
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| _version_ | 1866911466170351616 |
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| author | Erdogan, Yusuf H. Haque, Masudul |
| author_facet | Erdogan, Yusuf H. Haque, Masudul |
| contents | We consider non-Hermitian tight-binding one-dimensional Hamiltonians and show that imposing a certain symmetry causes all eigenvalues to pair up and the corresponding eigenstates to coalesce in pairs. This Pairwise Coalescence (PC) is an enhanced version of an exceptional point -- the complete spectrum pairs up, not just one pair of eigenstates. The symmetry is that of reflection excluding the central two sites, and allowing flipping of non-reciprocal hoppings (``generalized off-center reflection symmetry''). Two simple examples of PC exist in the literature -- our construction encompasses these examples and extends them to a vast class of Hamiltonians. We study several families of such Hamiltonians, extend to cases of full-spectrum higher-order coalescences, and show how the PC point corresponds to amplified non-orthogonality of the eigenstates and enhanced loss of norm in time evolution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06305 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Supercharging exceptional points: Full-spectrum pairwise coalescence in non-Hermitian systems Erdogan, Yusuf H. Haque, Masudul Quantum Physics We consider non-Hermitian tight-binding one-dimensional Hamiltonians and show that imposing a certain symmetry causes all eigenvalues to pair up and the corresponding eigenstates to coalesce in pairs. This Pairwise Coalescence (PC) is an enhanced version of an exceptional point -- the complete spectrum pairs up, not just one pair of eigenstates. The symmetry is that of reflection excluding the central two sites, and allowing flipping of non-reciprocal hoppings (``generalized off-center reflection symmetry''). Two simple examples of PC exist in the literature -- our construction encompasses these examples and extends them to a vast class of Hamiltonians. We study several families of such Hamiltonians, extend to cases of full-spectrum higher-order coalescences, and show how the PC point corresponds to amplified non-orthogonality of the eigenstates and enhanced loss of norm in time evolution. |
| title | Supercharging exceptional points: Full-spectrum pairwise coalescence in non-Hermitian systems |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2411.06305 |