Skin Localization Length
—
ξ = 1/ln(t_R/t_L)
NH-SSH Hamiltonian:
H = Σ (t_R c†_{n+1}c_n + t_L c†_n c_{n+1})
Bulk topology:
W = (1/2πi)∮ ∂_k ln det H dk
Skin modes: |ψ_n| ~ (t_L/t_R)^n
All bulk modes localize at boundary!
H = Σ (t_R c†_{n+1}c_n + t_L c†_n c_{n+1})
Bulk topology:
W = (1/2πi)∮ ∂_k ln det H dk
Skin modes: |ψ_n| ~ (t_L/t_R)^n
All bulk modes localize at boundary!
Unlike Hermitian systems, ALL eigenstates of a non-Hermitian lattice can localize at one edge — the skin effect. The PBC spectrum forms a loop in the complex plane; OBC spectrum collapses inside.