Winding Topology of Multifold Exceptional Points

• URL: http://arxiv.org/abs/2409.09153v2
• Date: Wed, 29 Jan 2025 10:19:40 GMT
• Title: Winding Topology of Multifold Exceptional Points
• Authors: Tsuneya Yoshida, J. Lukas K. König, Lukas Rødland, Emil J. Bergholtz, Marcus Stålhammar,
• Abstract summary: We characterize generic EP$n$s and symmetry-protected EP$n$s for arbitrary $n$. Our framework implies fundamental doubling theorems for both generic EP$n$s and symmetry-protected EP$n$s in $n$-band models.
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• Abstract: 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.

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