Winding topology of multifold exceptional points - Tsuneya Yoshida; J. Lukas K. König; Lukas Rødland; Emil J. Bergholtz; Marcus Stålhammar (Physical Review Research)
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.