New su(2) × su(2) integrable models

Some theories have, in addition to momentum and energy, other conserved charges. These theories are said integrable and can be exactly solved. The main ingredient of an integrable theory is an object called R-matrix which satisfies the so-called Yang-Baxter equation. After a brief review of integrable models, we will introduce a new method to find solutions of the Yang-Baxter equation and use it to compute the R-matrices with su(2) × su(2) symmetry. Using this method we were able to find new interesting integrable models, as well as some new generalizations of the Hubbard model.