Winding topology of multifold exceptional points
Despite their ubiquity, a systematic classification of multifold exceptional points, n-fold spectral degeneracies (EPns), remains a significant unsolved problem. In this article, we characterize the Abelian eigenvalue topology of generic EPns and symmetry-protected EPns for arbitrary n. The former a...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-01-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.7.L012021 |
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| author | Tsuneya Yoshida J. Lukas K. König Lukas Rødland Emil J. Bergholtz Marcus Stålhammar |
| author_facet | Tsuneya Yoshida J. Lukas K. König Lukas Rødland Emil J. Bergholtz Marcus Stålhammar |
| author_sort | Tsuneya Yoshida |
| collection | DOAJ |
| description | Despite their ubiquity, a systematic classification of multifold exceptional points, n-fold spectral degeneracies (EPns), remains a significant unsolved problem. In this article, we characterize the Abelian eigenvalue topology of generic EPns and symmetry-protected EPns for arbitrary n. The former and the latter emerge in (2n−2)- and (n−1)-dimensional parameter spaces, respectively. By introducing topological invariants called resultant winding numbers, we elucidate that these EPns are stable due to topology of a map from a base space (momentum or parameter space) to a sphere defined by resultants. In a D-dimensional parameter space (D≥c), the resultant winding numbers topologically characterize (D−c)-dimensional manifolds of generic (symmetry-protected) EPns, whose codimension is c=2n−2 (c=n−1). Our framework implies fundamental doubling theorems for both generic EPns and symmetry-protected EPns in n-band models. |
| format | Article |
| id | doaj-art-08b6b91b80764be1a68ff53c295caa7d |
| institution | Kabale University |
| issn | 2643-1564 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj-art-08b6b91b80764be1a68ff53c295caa7d2025-01-24T15:05:11ZengAmerican Physical SocietyPhysical Review Research2643-15642025-01-0171L01202110.1103/PhysRevResearch.7.L012021Winding topology of multifold exceptional pointsTsuneya YoshidaJ. Lukas K. KönigLukas RødlandEmil J. BergholtzMarcus StålhammarDespite their ubiquity, a systematic classification of multifold exceptional points, n-fold spectral degeneracies (EPns), remains a significant unsolved problem. In this article, we characterize the Abelian eigenvalue topology of generic EPns and symmetry-protected EPns for arbitrary n. The former and the latter emerge in (2n−2)- and (n−1)-dimensional parameter spaces, respectively. By introducing topological invariants called resultant winding numbers, we elucidate that these EPns are stable due to topology of a map from a base space (momentum or parameter space) to a sphere defined by resultants. In a D-dimensional parameter space (D≥c), the resultant winding numbers topologically characterize (D−c)-dimensional manifolds of generic (symmetry-protected) EPns, whose codimension is c=2n−2 (c=n−1). Our framework implies fundamental doubling theorems for both generic EPns and symmetry-protected EPns in n-band models.http://doi.org/10.1103/PhysRevResearch.7.L012021 |
| spellingShingle | Tsuneya Yoshida J. Lukas K. König Lukas Rødland Emil J. Bergholtz Marcus Stålhammar Winding topology of multifold exceptional points Physical Review Research |
| title | Winding topology of multifold exceptional points |
| title_full | Winding topology of multifold exceptional points |
| title_fullStr | Winding topology of multifold exceptional points |
| title_full_unstemmed | Winding topology of multifold exceptional points |
| title_short | Winding topology of multifold exceptional points |
| title_sort | winding topology of multifold exceptional points |
| url | http://doi.org/10.1103/PhysRevResearch.7.L012021 |
| work_keys_str_mv | AT tsuneyayoshida windingtopologyofmultifoldexceptionalpoints AT jlukaskkonig windingtopologyofmultifoldexceptionalpoints AT lukasrødland windingtopologyofmultifoldexceptionalpoints AT emiljbergholtz windingtopologyofmultifoldexceptionalpoints AT marcusstalhammar windingtopologyofmultifoldexceptionalpoints |