Entanglement structures in disordered chains of nitrogen-vacancy centers

A recent study [Phys. Rev. B 17 174111 (2022)] has hypothesized the assembly, along a specific type of one-dimensional defects of diamond, of chains of nitrogen-vacancy (NV) centers, potentially enabling the creation of qubit registers via their dipole-coupled electron spins. Here we investigate the connectivity of chains of up to ten coupled spins, mediated by the bi- and multipartite entanglement of their eigenstates. Rather conveniently, for regularly spaced spins the vast majority of the eigenstates displays strong connectivity, especially towards the center of the spectrum and for longer chains. Furthermore, positional disorder can change, and possibly reduce, the connectivity of the register, but seldom suppresses it.