The presence of Yang-Baxter integrability in a given model provides a series of powerful tools to study its spectrum and properties. This is the case, for instance, in a series of discrete models called integrable spin chains. Examples include the Hubbard model, the Potts model and the Heisenberg spin chain. For most systems of this type, a particle in a given site of the chain only interacts with the ones in its first neighbour sites; they are called Nearest-Neighbour spin chains. Certain applications in gauge theories and statistical physics, however, require understanding long-range deformations.
In this talk, I will start with an introduction to the Yang-Baxter equation and integrable spin chains. I will then present a procedure to include long-range interactions such that integrability is perturbatively preserved at each order. I will show two examples: the spin-1/2 and the spin-1 isotropic chains, and discuss their properties.
