Non-Abelian monopole in the parameter space of point-like interactions

We study non-Abelian geometric phase in N=2 supersymmetric quantum mechanics for a free particle on a circle with two point-like interactions at antipodal points. We show that non-Abelian Berry’s connection is that of SU(2) magnetic monopole discovered by Moody, Shapere and Wilczek in the context of adiabatic decoupling limit of diatomic molecule. •Supersymmetric quantum mechanics is an ideal playground for studying geometric phase.•We determine the parameter space of supersymmetric point-like interactions.•Berry’s connection is given by a Wu–Yang-like magnetic monopole in SU(2) Yang–Mills.