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Topological charge pumping occurs in the adiabatic limit, and thenon-adiabatic effect due to finite ramping velocity reduces the pumpingefficiency and leads to deviation from quantized charge pumping. In this work,we discuss the relation between this deviation from quantized charge pumpingand the entanglement generation after a pumping circle. In this simplestsetting, we show that purity $\mathcal{P}$ of the half system reduced densitymatrix equals to $\mathcal{R}$ defined as $(1-\kappa)^2+\kappa^2$, where$\kappa$ denotes the pumping efficiency. In generic situations, we argue$\mathcal{P}<\mathcal{R}$ and the pumping efficiency can provide an upper boundfor purity and, therefore, a lower bound for generated entanglement. To supportthis conjecture, we propose a solvable pumping scheme in theRice--Mele--Hubbard model, which can be represented as brick-wall type quantumcircuit model. With this pumping scheme, numerical calculation of chargepumping only needs to include at most six sites, and therefore, the interactionand the finite temperature effects can be both included reliably in the exactdiagonalization calculation. The numerical results using the solvable pumpingcircle identify two regimes where the pumping efficiency is sensitive toramping velocity and support the conjecture $\mathcal{P}<\mathcal{R}$ when bothinteraction and finite temperature effects are present.

Non-Adiabatic Effect in Topological and Interacting Charge Pumping