The course gives an introduction to the theory of quantum phase transition in interacting many body systems and to Renormalization Group. In the first part one dimensional models are introduced like quantum spin chains (XX or XY models) and the Luttinger model. In the second part we analyze by Renormalization Group methods theories with non trivial fixed point, like phi4 or XYZ, and the concepts of emerging synnmetries and Ward Identities are introduced.
Expected learning outcomes
At the end of the course the student will be able for instance: 1)To use the Jordan-Wigner transformation and compute thermodynamical averages in spin chains 2)to use bosonization and compute the correlations in Luttinger models 4)To compute the beta function and the critical exponents of phi4 by epsilon expansion 5)To derive and use Ward Identites 6)To analyze by Renormalization Group many body fermionic interacting models.
Lesson period: First semester
(In case of multiple editions, please check the period, as it may vary)