The spin-s homogeneous central spin model: Exact spectrum and dynamics

We consider the problem of a central spin with arbitrary spin s that interacts pairwise and uniformly with a bath of N spins with s = 1/2. We present two approaches for determining the exact spectrum of this model, one based on properties of , and the other based on integrability. We also analyze the exact time evolution of a spin coherent state, and compute the time evolution of various quantities of physical interest, including the entanglement entropy, spin polarization and Loschmidt echo.