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

TL;DR

This paper investigates how static disorder affects topological charge pumping in the Rice-Mele model, revealing that disorder can cause breakdown of quantization even without delocalization, and introduces a new way to identify topological transitions.

Contribution

It demonstrates that the local Chern marker effectively detects topological transitions in disordered systems and shows that quantized pumping breaks down when the spectral gap closes, independent of localization.

Findings

Local Chern marker accurately detects topological transitions.

Disorder-driven breakdown of quantized charge pumping occurs with gap closing.

Average bulk gap overestimates stability; typical gap provides better estimate.

Abstract

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. In the instantaneous basis, we compute the polarization, the entanglement spectrum, and the 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 and 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.