Non-Hermitian Skin Effect — Hatano-Nelson Model

The Hatano-Nelson model has asymmetric hopping: amplitude t+g rightward, t−g leftward. Under open boundary conditions (OBC), ALL eigenstates pile up at one boundary — the "skin effect". Under periodic BC (PBC), eigenstates are plane waves. The OBC spectrum is a line segment while PBC spectrum is a loop in the complex plane.

H_HN = Σ_n [(t+g)|n+1⟩⟨n| + (t-g)|n⟩⟨n+1|]

Chain length N30

Hopping t1.50

Asymmetry g0.80

On-site disorder W0.00

Skin length ξ: —

|t+g|/|t-g|: —

PBC gap: —