# Finite-size corrections to quantized particle transport in topological charge pumps

## TL;DR

This paper analyzes how finite system sizes affect the quantization of charge transport in topological pumps, deriving corrections and showing how to minimize them through protocol design.

## Contribution

It provides a theoretical framework for finite-size corrections in topological charge pumps, applicable to both non-interacting and interacting systems.

## Key findings

- Finite-size corrections depend on system details.
- Proper protocols can suppress finite-size effects.
- Corrections are significant even in large systems.

## Abstract

We investigate the quantization of adiabatic charge transport in the insulating ground state of finite systems. Topological charge pumps are used in experiments as an indicator of topological order. In the thermodynamic limit the transport can be related to a topological Berry phase and is thus strictly quantized. This is no longer true for finite systems. We derive finite-size corrections to the transport both for non-interacting and interacting systems and relate them to analytic properties of the single- and many-body Berry curvature. We find that they depend on the details of experimental realizations of the pumps. While they can be non-negligible even in large systems, a proper choice of the pumping protocol can suppress these corrections.