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We calculate the charge gap $\Delta E_C$ and the spin gap $\Delta E_S$ of theionic Hubbard chain including electron-hole symmetric density-dependenthopping. The vanishing of $\Delta E_C$ ($\Delta E_S$) signals a quantumcritical point (QCP) in the charge (spin) sector. Between both critical points,the system is a fully gapped spontaneously dimerized insulator (SDI). We focusour study in this region. Including alternation in the hopping, it is possibleto perform an adiabatic Thouless pump of one charge per cycle, but with avelocity limited by the size of the gaps.

Charge and spin gaps of the ionic Hubbard model with density-dependent hopping