SSH model and winding number
A one-dimensional dimerized chain has distinct gapped winding sectors.
$$H(k)=(t_1+t_2\cos k)\sigma_x+t_2\sin k\,\sigma_y$$
What this means
A one-dimensional dimerized chain has distinct gapped winding sectors.
Deep dive: mathematical and physical mechanism
Chiral symmetry forbids a $\sigma_z$ term. The vector $(d_x,d_y)$ winds around the origin when $|t_2|>|t_1|$. Its integer winding changes only when the bulk gap closes at $|t_1|=|t_2|$. An open chain with suitable termination can host end states.
How it appears in quantum phenomena
Polyacetylene-inspired electronic, mechanical, and photonic lattices.
Assumptions, caveats and limitations
End-state existence and energy depend on termination and protection by chiral symmetry.
Connect the ideas
For context, see the Topological Band Theory topic guide and the reading references.