Orateur
Description
In this work, we investigate nearest-neighbour deformations of integrable models. In our previous paper, ’On deforming and breaking integrability’ (2603.17018), we established the framework to construct deformation terms that satisfy the commutation relations of conserved charges through an order-by-order expansion of the Hamiltonian using the Boost Operator method, applying this framework to the XXZ model. In this presentation, I will review these results, demonstrating that such deformations naturally fall into three distinct classes: those that break integrability, those that strictly preserve it, and those that remain integrable only perturbatively up to a given order. Finally, I will present the new results of our current work, which extends this formalism to the one-dimensional Hubbard model. We will discuss the physical and algebraic properties arising from this new application, highlighting the structure of the quasi-integrable deformations.