Hatano-Nelson model — asymmetric hopping drives boundary localization
The Hatano-Nelson model has asymmetric hopping: t_R = t·e^γ rightward, t_L = t·e^{-γ} leftward. Under open boundary conditions (OBC), ALL eigenstates exponentially localize at one boundary — the non-Hermitian skin effect. The OBC and PBC spectra are topologically distinct: PBC gives an annular loop with winding number W=±1; OBC collapses it to a line segment. This spectral topology is the origin of skin localization.