Perfect State Transfer from a Localised Two-Excitation State to a Dicke State via Static Spin-Network Hamiltonians

I construct a family of time-independent, excitation-preserving spin Hamiltonians that realises perfect state transfer from a localised two-excitation state to the symmetric two-excitation Dicke state, for every system size $N \ge 4$. The Hamiltonian has the physical form $H = \sum_{i<j} J_{ij} (σ_i