  The fast forward scheme of adiabatic quantum dynamics is applied to finite
regular spin clusters with various geometries and the nature of driving
interactions is elucidated. The fast forward is the quasi-adiabatic dynamics
guaranteed by regularization terms added to the reference Hamiltonian, followed
by a rescaling of time with use of a large scaling factor. With help of the
regularization terms consisting of pair-wise and 3-body interactions, we apply
the proposed formula (Phys. Rev.A 96, 052106(2017)) to regular triangle and
open linear chain for N = 3 spin systems, and to triangular pyramid, square,
primary star graph and open linear chain for N = 4 spin systems. The
geometry-induced symmetry greatly decreases the rank of coefficient matrix of
the linear algebraic equation for regularization terms. Choosing a transverse
Ising Hamiltonian as a reference, we find: (1) for N = 3 spin clusters, the
driving interaction consists of only the geometry-dependent pairwise
interactions and there is no need for the 3-body interaction; (2) for N = 4
spin clusters, the geometry-dependent pair-wise interactions again constitute
major part of the driving interaction, whereas the universal 3-body interaction
free from the geometry is necessary but plays a subsidiary role. Our scheme
predicts the practical driving interaction in accelerating the adiabatic
quantum dynamics of structured regular spin clusters.
