Ground-State Analysis for an Exactly Solvable Coupled-Spin Hamiltonian

We introduce a Hamiltonian for two interacting $\mathfrak{su}(2)$ spins. We use a mean-field analysis and exact Bethe ansatz results to investigate the ground-state properties of the system in the classical limit, defined as the limit of infinite spin (or highest weight). Complementary insights are provided through investigation of the energy gap, ground-state fidelity, and ground-state entanglement, which are numerically computed for particular parameter values. Despite the simplicity of the model, a rich array of ground-state features are uncovered. Finally, we discuss how this model may be seen as an analogue of the exactly solvable $p+ip$ pairing Hamiltonian.