SSH Model — Topological Edge States

The Su-Schrieffer-Heeger (SSH) model is the simplest topological insulator: a 1D chain with alternating hopping amplitudes v (intracell) and w (intercell). When w > v, the bulk winding number ν = 1 and protected zero-energy edge states appear at both ends of a finite chain.

v = 0.5
w = 1.0
w/v = 2.0
Winding ν: 1
Phase: Topological
Gap: —
Edge states: 2
Bulk-boundary correspondence:
ν = 1 ↔ 2 zero-modes at edges
ν = 0 ↔ no edge states

Transition at v = w (gap closes)
Zero modes: energy |E|<0.01
H = v∑(A†B) + w∑(B†A_next)
Bulk: E(k)=±√(v²+w²+2vw cos k)
Gap = 2|w-v|