Why finite-size non-Hermitian eigenvalues can miss asymptotic eigenstates in topological physics
Non-Hermitian systems show a spectral dichotomy where eigenvalues and eigenstates differ in the thermodynamic limit. The Hatano-Nelson model proves that finite-size eigenvalue calculations miss many asymptotic eigenstates. This suggests that focusing on eigenstate spectra provides a more stable and complete characterization of non-Hermitian topology than relying solely on eigenvalues.