  This paper introduces a theoretical framework for understanding the
accumulation of non-Abelian geometric phases in rotating nitrogen-vacancy
centers in diamond. Specifically, we consider how degenerate states can be
achieved and demonstrate that the resulting geometric phase for multiple paths
is non-Abelian. We find that the non-Abelian nature of the phase is robust to
fluctuations in the path and magnetic field. In contrast to previous studies of
the accumulation of Abelian geometric phases for nitrogen-vacancy centers under
rotation we find that the limiting time-scale is $T_{1}$. As such a non-Abelian
geometric phase accumulation in nitrogen-vacancy centers has potential
advantages for applications as gyroscopes.
