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It is shown in a recent preprint [arXiv:2001.10008] that the central spinmodel with XX-type qubit-bath coupling is integrable for a central spin$s_0=1/2$. Two types of eigenstates, separable states (dark states) andentangled states (bright states) between the central spin and the bath spins,are manifested. In this work, we show by using an operator product stateapproach that the XX central spin model with central spin $s_0>1/2$ andinhomogeneous coupling is partially solvable. That is, a subset of theeigenstates are obtained by the operator product state ansatz. These are theseparable states and those entangled states in the single-spin-excitationsubspace with respect to the fully polarized reference state. Due to the highdegeneracy of the separable states, the resulting Bethe ansatz equations arefound to be non-unique. In the case of $s_0=1/2$ we show that all the separableand entangled states can be written in terms of the operator product states,recovering the results in [arXiv:2001.10008]. Moreover, we also apply ourmethod to the case of homogeneous coupling and derive the corresponding Betheansatz equations.

Separable and entangled states in the high-spin XX central spin model