Spin and entanglement dynamics in the central-spin model with homogeneouscouplings

Abstract

We calculate exactly the time-dependent reduced density matrix for the central spin in thecentral-spin model with homogeneous Heisenberg couplings. Therefrom, the dynamicsand the entanglement entropy of the central spin are obtained. A rich variety ofbehaviours are found, depending on the initial state of the bath spins. For an initiallyunpolarized unentangled bath, the polarization of the central spin decays to zero in thethermodynamic limit, while its entanglement entropy becomes maximal. On theother hand, if the unpolarized environment is initially in an eigenstate of thetotal bath spin, the central spin and the entanglement entropy exhibit persistentmonochromatic large-amplitude oscillations. This raises the question of to whatextent entanglement of the bath spins prevents decoherence of the central spin.