  We investigate topological charge pumping in a system of interacting bosons
in the tight-binding limit, described by the Rice-Mele model. An appropriate
topological invariant for the many-body case is the change of polarization per
pump cycle, which we compute for various interaction strengths from
infinite-size matrix-product-state simulations. We verify that the charge
pumping remains quantized as long as the pump cycle avoids the superfluid
phase. In the limit of hardcore bosons, the quantized pumped charge can be
understood from single-particle properties such as the integrated Berry
curvature constructed from Bloch states, while this picture breaks down at
finite interaction strengths. These two properties -- robust quantized charge
transport in an interacting system of bosons and the breakdown of a
single-particle invariant -- could both be measured with ultracold quantum
gases extending a previous experiment [Lohse et al., Nature Phys. 12, 350
(2016)]. Furthermore, we investigate the entanglement spectrum of the Rice-Mele
model and argue that the quantized charge pumping is encoded in a winding of
the spectral flow in the entanglement spectrum over a pump cycle.
