Protection of all nondefective twofold degeneracies by antiunitary symmetries in non-Hermitian systems
Non-Hermitian degeneracies are classified as defective exceptional points (EPs) and nondefective degeneracies. While in defective EPs, both eigenvalues and eigenvectors coalesce, nondefective degeneracies are characterized merely by the emergence of degenerate eigenvalues. It is also known that all...
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| Format: | Article |
| Language: | English |
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American Physical Society
2022-12-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.4.043213 |
| _version_ | 1797210564853760000 |
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| author | Sharareh Sayyad |
| author_facet | Sharareh Sayyad |
| author_sort | Sharareh Sayyad |
| collection | DOAJ |
| description | Non-Hermitian degeneracies are classified as defective exceptional points (EPs) and nondefective degeneracies. While in defective EPs, both eigenvalues and eigenvectors coalesce, nondefective degeneracies are characterized merely by the emergence of degenerate eigenvalues. It is also known that all degeneracies are either symmetryprotected or accidental. In this paper, I prove that antiunitary symmetries protect all nondefective twofold degeneracies. By developing a 2D non-Hermitian tight-binding model, I have demonstrated that these symmetries comprise various symmetry operations, such as discrete or spatial point-group symmetries and Wick's rotation in the non-Hermitian parameter space. Introducing these composite symmetries, I present the protection of nondefective degeneracies in various parameter regimes of my model. This work paves the way to stabilizing nondefective degeneracies and offers a new perspective on understanding non-Hermitian band crossings. |
| first_indexed | 2024-04-24T10:12:36Z |
| format | Article |
| id | doaj.art-36d5983c11774db781144661d0b78760 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:12:36Z |
| publishDate | 2022-12-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-36d5983c11774db781144661d0b787602024-04-12T17:27:18ZengAmerican Physical SocietyPhysical Review Research2643-15642022-12-014404321310.1103/PhysRevResearch.4.043213Protection of all nondefective twofold degeneracies by antiunitary symmetries in non-Hermitian systemsSharareh SayyadNon-Hermitian degeneracies are classified as defective exceptional points (EPs) and nondefective degeneracies. While in defective EPs, both eigenvalues and eigenvectors coalesce, nondefective degeneracies are characterized merely by the emergence of degenerate eigenvalues. It is also known that all degeneracies are either symmetryprotected or accidental. In this paper, I prove that antiunitary symmetries protect all nondefective twofold degeneracies. By developing a 2D non-Hermitian tight-binding model, I have demonstrated that these symmetries comprise various symmetry operations, such as discrete or spatial point-group symmetries and Wick's rotation in the non-Hermitian parameter space. Introducing these composite symmetries, I present the protection of nondefective degeneracies in various parameter regimes of my model. This work paves the way to stabilizing nondefective degeneracies and offers a new perspective on understanding non-Hermitian band crossings.http://doi.org/10.1103/PhysRevResearch.4.043213 |
| spellingShingle | Sharareh Sayyad Protection of all nondefective twofold degeneracies by antiunitary symmetries in non-Hermitian systems Physical Review Research |
| title | Protection of all nondefective twofold degeneracies by antiunitary symmetries in non-Hermitian systems |
| title_full | Protection of all nondefective twofold degeneracies by antiunitary symmetries in non-Hermitian systems |
| title_fullStr | Protection of all nondefective twofold degeneracies by antiunitary symmetries in non-Hermitian systems |
| title_full_unstemmed | Protection of all nondefective twofold degeneracies by antiunitary symmetries in non-Hermitian systems |
| title_short | Protection of all nondefective twofold degeneracies by antiunitary symmetries in non-Hermitian systems |
| title_sort | protection of all nondefective twofold degeneracies by antiunitary symmetries in non hermitian systems |
| url | http://doi.org/10.1103/PhysRevResearch.4.043213 |
| work_keys_str_mv | AT shararehsayyad protectionofallnondefectivetwofolddegeneraciesbyantiunitarysymmetriesinnonhermitiansystems |