Adiabatic Thouless pumping in rapid-cycle protocols

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.
In this talk, focusing on the Rice-Mele insulator I introduce 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.
Based on arxiv 2104.02751