Singularities of Berry connections inhibit the accuracy of the adiabatic approximation

Adiabatic approximation for quantum evolution is investigated addressing its dependence on the Berry connections that are functions of a slowly-varying parameter R. When the Berry connections have singularities of type 1/R-sigma with sigma < 1, the adiabatic fidelity converges to unit according to a power-law; When the singularity index a becomes larger than one, adiabatic approximation breaks down. Two-level models are used to substantiate our theory. (C) 2007 Elsevier B.V. All rights reserved.