The Geometry of (non) abelian adiabatic pumping

Details The Geometry of (non) abelian adiabatic pumping The Geometry of (non) abelian adiabatic pumping

2010-12-24

arxiv.org/abs/1012.5384v3

J.Phys.A44:295301,2011

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

17 pages, 7 figures

Scientific paper

10.1088/1751-8113/44/29/295301

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.

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