SSH Model — Topological Winding Number

Su-Schrieffer-Heeger chain: topological insulator in 1D with winding number W=0 (trivial) or W=1 (topological) — bulk-boundary correspondence

W=0

Winding number

—

Band gap

Trivial

Topological phase

Edge states

Intracell hopping v 0.50

Intercell hopping w 1.50

On-site disorder δ 0.00

Chain length N 20

The SSH model (Su-Schrieffer-Heeger 1979) describes a 1D chain with alternating hoppings v (intracell) and w (intercell). The bulk Hamiltonian H(k) traces a circle in the (d_x,d_y) plane as k traverses the BZ. The winding number W = how many times it winds around the origin: W=0 if |v|>|w| (trivial), W=1 if |w|>|v| (topological). Bulk-boundary correspondence: W=1 guarantees zero-energy edge states.