We show through selected examples, relevant to the physics of fullerene ions, that the presence of a Berry phase in dynamical Jahn-Teller systems does not guarantee the degeneracy of the ground state, contrary to what previously believed. Moreover, we introduce a new class of JahnTeller systems with no Berry phase, as a generalization of the basic icosahedral H ⊗ h case.

In this letter we have pointed out that frustration in spin glass is realized through the Berry phase due to the conflict between the spin ordering in the course of parallel transport of spinor. We have came to the point that the Berry phase depicting the chiral change of helicity of a quantized spinor is prominent only in the presence of frustration.