Integer charge quantized by Chern number as Hamiltonian is cycled adiabatically
In a Rice-Mele model, slowly cycling the parameter φ from 0→2π pumps exactly one electron per unit cell per cycle — regardless of details.
This integer is the first Chern number of the occupied band's Berry connection over the (k, φ) torus. Even with disorder, Q ∈ ℤ exactly.
The pumping is the 1D analogue of the quantum Hall effect (TKNN invariant), discovered by Thouless 1983.