Dynamically Robust Counterdiabatic Topological Pumping

Abstract

Thouless pumping is a transport phenomenon whereby an insulating, time-periodic Hamiltonian induces a robustly quantized transfer of charge, per driving cycle, in the quasi-adiabatic limit. In this work we apply the shortcuts to adiabaticity (STA) method of counterdiabatic (CD) driving to the Rice-Mele model, an archetypal model for Thouless pumping. We show that the charge pumped rapidly across each bond of our CD Rice-Mele model is robustly quantized and determined by a Chern number. The CD Hamiltonian generally involves long-range, hence non-local, hopping. Therefore we also derive an exact, local, nearest-neighbor CD Hamiltonian for our lattice system. We show that our nearest neighbor non-adiabatic protocol possesses the same topological robustness to onsite disorder as quasi-adiabatic Thouless pumps and is moreover surprisingly robust to onsite disorder and noise errors in implementing the CD protocol, for sufficiently rapid driving. The protocol also reproduces finite-temperature Thouless pump results away from the adiabatic limit. In addition, we develop a general method to produce non-trivial, finite-time quantized pumping starting from any Rice-Mele initial ground state using only nearest-neighbor hopping.

25 pages, 7 figures