Thouless Topological Pump — Rice-Mele Model

Adiabatic charge transport quantized by Chern number. One pump cycle moves exactly one charge quantum across the chain.

Chain sites N 20 Pump phase φ 0.00π Hopping asymmetry δ 0.50 On-site potential Δ 0.50

Charge pumped: 0.00e

H = Σ[J(1±δcos φ)c†c + Δsin(φ)(nᵢ-½)]

Rice-Mele model (1982): 1D chain with alternating hopping + staggered potential, parametrized by φ. Thouless (1983): adiabatic cycle pumps exactly C=1 electron. Chern number = winding of Zak phase over BZ.