  A non-contractible adiabatic cycle performed in the parameter space of a
one-dimensional band insulator is known to result in a noise-free transfer of
an integral multiple of charge across the length of the system. Such quantized
pumping requires suppression of quasiparticle production, which can in theory
be achieved in the limit of infinitely slow driving. Here, focusing on the
Rice-Mele insulator, we construct a continuous family of finite-frequency
pumping protocols which ensure both the absence of excitations and the perfect
quantization of the pumped charge at the end of a cycle. The family, which
contains an adiabatic protocol as a limiting case, is obtained through a
mapping of the problem onto the Lax representation of the Euclidean sinh-Gordon
equation.
