Fast-forward approach to adiabatic quantum dynamics of regular spin clusters: Nature of geometry-dependent driving interactions
Abstract
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. Fast forward is the quasiadiabatic dynamics guaranteed by regularization terms added to the reference Hamiltonian, followed by a rescaling of time with the use of a large scaling factor. With the help of the regularization terms consisting of pairwise and three-body interactions, we apply the proposed formula [I. Setiawan et al., Phys. Rev. A 96, 052106 (2017)] to regular triangle and open linear chains for $N=3$ spin systems and to triangular pyramid, square, primary star graph, and open linear chains for $N=4$ spin systems. The geometry-induced symmetry greatly decreases the rank of the coefficient matrix of the linear algebraic equation for regularization terms. Choosing a transverse Ising Hamiltonian as a reference, we find, for $N=3$ spin clusters, that the driving interaction consists of only the geometry-dependent pairwise interactions and there is no need for the three-body interaction and, for $N=4$ spin clusters, that the geometry-dependent pairwise interactions again constitute a major part of the driving interaction, whereas the universal three-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.