Ground-state and dynamical properties of a spin-$S$ Heisenberg star

Abstract

is an interacting central spin model composed of a spin-1/2 central spin and a homogeneously coupled XXX ring. In this work, we generalize the spin-1/2 Heisenberg star to the case of arbitrary S < N/2, where S is the size of the central spin and N is the number of spins-1/2 in the XXX spin bath. We obtain all the eigenenergies and explicit expressions of the sub-ground states in each l-subspace with l being the total angular momentum of the bath. The absolute ground-state energy and the corresponding bath angular momentum l as functions of the intrabath coupling are numerically calculated for N = 16 and S = 1, 2, • • • , 7 and their behaviors are quantitatively explained in the weak and strong intrabath coupling limits. By including a Zeeman term for the central spin and the anisotropy in the intrabath coupling, we also study the polarization dynamics of the central spin for a bath initially prepared in the spin coherent state. Under the resonant condition and at the isotropic point of the bath, the polarization dynamics for S > 1/2 exhibits collapse-revival behaviors with fine structures. However, the collapse-revival phenomena is found to be fragile with respect to anisotropy of the intrabath coupling.