Fig. 8: Diagnostic verification of the loop and the branch cut.
a, b The tracked relative phase of eigenvalues (poles) for the non-Hermitian approximation (NHA) and the exact case, respectively. Blue circles and brown crosses represent the case of NS = 80 and NS = 300, respectively. c, d The corresponding winding number (red circles) for the NHA and exact case, with ω = − 1 − ωii, where ωi ∈ [0.08, 0.16]. These results confirm the presence of loop and branch cut characteristics.
