Non-Hermitian Skin Effect

In non-Hermitian systems with asymmetric hopping, all bulk eigenstates collapse to the boundary — the skin effect. The bulk spectrum under periodic boundary conditions (PBC) traces a loop in the complex plane; the winding number W of this loop determines the number of skin modes.

t_R = 1.00
t_L = 0.50
γ = 0.00
N = 20
Hamiltonian: H = Σ(t_R|n+1⟩⟨n| + t_L|n⟩⟨n+1|) + iγ|n⟩⟨n|
PBC spectrum: E(k) = t_R·e^{ik} + t_L·e^{-ik} → loop in ℂ plane
Winding number W = ∮ d(arg E) / 2π → |W| skin modes pile at boundary