The Geometry of (non) abelian adiabatic pumping

TL;DR

This paper introduces a geometric gauge framework for adiabatic charge pumping in closed systems, encompassing Abelian and non-Abelian cases, with practical algorithms and a demonstrative four-state model analysis.

Contribution

It provides a novel geometric gauge description and a simple numerical algorithm for adiabatic pumping, including non-Abelian processes, validated on a four-state model.

Findings

Discretized holonomies are computationally accessible.

The geometric approach offers new insights into charge pumping.

Application to a four-state model demonstrates practical relevance.

Abstract

We give a gauge description of the adiabatic charge pumping in closed systems, both in Abelian and non-Abelian processes, and by means of asymptotic Wilson loops in a suitable parameter manifold. Our geometric formulation provides new insights into this issue, and a very simple algorithm for numerical computations. Indeed, as we show first, discretized Berry--Wilczeck--Zee holonomies are easy to implement. Finally, we study non-Abelian pumping in a solvable four-state model, already used in several contexts, to demonstrate the relevance of our approach.