Effect of disorder on topological charge pumping in the Rice-Mele model

Recent experiments with ultracold quantum gases have successfully realized integer-quantized topological charge pumping in optical lattices. Motivated by this progress, we study the effects of static disorder on topological Thouless charge pumping. We focus on the half-filled Rice-Mele model of free spinless fermions and consider random diagonal disorder. We use both static and time-dependent simulations to characterize the charge pump. The set of measures that we compute in the instantaneous basis include the polarization, the entanglement spectrum, and the space-integrated local Chern marker. As a first main result, we conclude that the space-integrated local Chern marker is best suited for a quantitative determination of topological transitions in a disordered system. In the time-dependent simulations we use the time-integrated current to obtain the pumped charge in slowly periodically driven systems. As a second main result, we observe and characterize a disorder-driven breakdown of the quantized charge pump. There is an excellent agreement between the static and the time-dependent ways of computing the pumped charge. The topological transition occurs well in the regime where all states are localized on the given system sizes. This observation is consistent with previous studies and the topological transition is therefore not tied to a delocalization-localization transition of Hamiltonian eigenstates. For individual disorder realizations, the breakdown of the quantized pumping occurs for parameters where the spectral bulk gap inherited from the band gap of the clean system closes, leading to a globally gapless spectrum. As a third main result and with respect to the analysis of finite-size systems, we show that the disorder average of the bulk gap severely overestimates the stability of quantized pumping. A much better estimate is the typical value of the distribution of energy gaps, also called mode of the distribution. We discuss our results in the context of recent quantum-gas experiments that realized charge pumps.

Automated summary

Recent experiments have shown integer-quantized topological charge pumping in ultracold quantum gases, motivating a study on the effects of static disorder on topological Thouless charge pumping. The study found that the space-integrated local Chern marker is best for quantitatively determining topological transitions in disordered systems, and observed a disorder-driven breakdown of the quantized charge pump. The analysis suggests that the stability of quantized pumping may be overestimated by the disorder average of the bulk gap, with the typical value of energy gap distribution providing a better estimate.