# Robustness of the pumping charge to dynamic disorder

## TL;DR

This paper demonstrates that the quantized pumping charge in a topological 1D Rice-Mele model remains robust despite dynamic disorder, highlighting the potential for experimental measurement of topological invariants in imperfect systems.

## Contribution

It introduces band correlation functions (BCFs) as robust local quantities and shows their stability under disorder, along with numerical evidence of quantized charge robustness in a disordered Rice-Mele model.

## Key findings

- BCFs are robust if the band gap remains open.
- Quantized pumping charge persists under dynamic disorder.
- Translational symmetry features can emerge in disordered systems.

## Abstract

We investigate the effect of disorder on a gapped crystalline system by introducing a class of local quantities for an energy band, which is referred as to band correlation function (BCF) and is the sum of correlation functions for all eigenstates of the band. We show that the BCFs are robust in the presence of disorder if the band gap is not collapse. The eigenstate set of an energy band can be almost completely mapped onto the perturbated eigenstate set, referred as to quasi-closed mapping, when it is sufficiently isolated from other bands. Some features relate to translational symmetry may emerge in a randomly perturbed system. We demonstrate this by simulating numerically the pumping process for a 1D Rice-Mele (RM) model with disorders on the hopping strength and on-site potential. It is shown that the quantized pumping charge is robust against with the dynamic disorder. This result indicates the possibility of measuring the topological invariant in experimental system with imperfection.