Doublons in 2D spin models

In the presence of strong interactions, two particles can bind together forming what became known as doublons. They move as a single particle, but slower. Doublons have been extensively studied in the Bose-Hubbard model, where the two bosons occupy the same site. We focus on spin models, where the doublon corresponds to a bound pair of excitations occupying neighboring sites. We explore different scenarios, where energy conservation would allow for different configurations in the plane, even for the splitting of the bound pair, such as when two doublons collide or when an impurity site is added to system, yet the doublons prove to be very robust and stick together. We illustrate our results using two-dimensional spin models.