Doublons in 1D Spin Models

In the presence of strong interactions, two particles can bind together forming what became known as doublons. Doublons are a pair of upspins that are either located next to each other, or connected like a ring. They move as a single particle, but slower as the energy levels increase. Doublons have been extensively studied in the Bose-Hubbard model, where the two bosons occupy the same site. We use the Hamiltonian Matrix to help conceputalize quantum systems. We also encorporate the Schrödinger and Dirac equations in order to follow the function of the electron-wave-equation. 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 not prevent the bound pair from splitting, such as when an impurity site is added to system, yet the doublons prove to be very robust and stick together. We illustrate our results using a chain of 1/2-spins.