traced back to the presence of isolated singularities in parameter space. Formally, Berry’s phase can be related to the curvature of the Hilbert space bundle over the base space of parameters [@Simon], and it is this interpretation of Berry’s phase which renders its potential usefulness as a diagnostic tool for criticality plausible: points of degeneracy are associated with a greater curvature of the associated Hilbert space bundle, and therefore it might be reasonable to expect Berry’s phase to act as a signature for quantum critical points in interacting spin systems.

Of course, the geometric phase of $N$ non-interacting spin-$1/2$ particles with respect to a particular circuit is simply $N$ times the geometric phase of a single particle, which in turn can be related to the circuit’s solid angle, as explained above. However, as we switch on the spin-spin interactions, this simple interpretation of the geometric phase in terms of solid angles starts to break down. It is of great interest to know how the geometric phase of a set of interacting spins with respect to a given circuit changes as a function of the coupling parameter, and whether the geometric phase is able to signal the presence of critical points 