Winding Topology of Multifold Exceptional Points
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916588449431552 |
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| author | Yoshida, Tsuneya König, J. Lukas K. Rødland, Lukas Bergholtz, Emil J. Stålhammar, Marcus |
| author_facet | Yoshida, Tsuneya König, J. Lukas K. Rødland, Lukas Bergholtz, Emil J. Stålhammar, Marcus |
| contents | Despite their ubiquity, a systematic classification of multifold exceptional points, $n$-fold spectral degeneracies (EP$n$s), remains a significant unsolved problem. In this article, we characterize the Abelian eigenvalue topology of generic EP$n$s and symmetry-protected EP$n$s for arbitrary $n$. The former and the latter emerge in a $(2n-2)$- and $(n-1)$-dimensional parameter space, respectively. By introducing topological invariants called resultant winding numbers, we elucidate that these EP$n$s 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 ($D\geq c$), the resultant winding number topologically characterize a $(D-c)$-dimensional manifold of generic [symmetry-protected] EP$n$s whose codimension is $c=2n-2$ [$c=n-1$]. Our framework implies fundamental doubling theorems for both generic EP$n$s and symmetry-protected EP$n$s in $n$-band models. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_09153 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Winding Topology of Multifold Exceptional Points Yoshida, Tsuneya König, J. Lukas K. Rødland, Lukas Bergholtz, Emil J. Stålhammar, Marcus Mesoscale and Nanoscale Physics Other Condensed Matter Quantum Gases Statistical Mechanics Quantum Physics Despite their ubiquity, a systematic classification of multifold exceptional points, $n$-fold spectral degeneracies (EP$n$s), remains a significant unsolved problem. In this article, we characterize the Abelian eigenvalue topology of generic EP$n$s and symmetry-protected EP$n$s for arbitrary $n$. The former and the latter emerge in a $(2n-2)$- and $(n-1)$-dimensional parameter space, respectively. By introducing topological invariants called resultant winding numbers, we elucidate that these EP$n$s 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 ($D\geq c$), the resultant winding number topologically characterize a $(D-c)$-dimensional manifold of generic [symmetry-protected] EP$n$s whose codimension is $c=2n-2$ [$c=n-1$]. Our framework implies fundamental doubling theorems for both generic EP$n$s and symmetry-protected EP$n$s in $n$-band models. |
| title | Winding Topology of Multifold Exceptional Points |
| topic | Mesoscale and Nanoscale Physics Other Condensed Matter Quantum Gases Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2409.09153 |