Course Unit Page

Academic Year 2020/2021

Learning outcomes

At the end of the course the student will acquire some knowledge about the physics of strongly interacting many body systems. More specifically he/she will be able to use both exact and approximation methods for the study of phase transitions and critical phenomena. These techniques will be seen in action by analysing some paradigmatic models, both in the classical and in the quantum setting.

Course contents


  • Review on classical phase transitions and introduction to quantum phase transitions
  • Spontaneous symmetry breaking and the Landau paradigm
  • Some examples: magnetism and superconductivity
  • BKT transitions; topological defects and vortices
  • Topological phase transitions and examples (SSH and Kitaev chain, p-wave superconductors in 2d); Berry phase and topological Chern insulators


  • Green’s functions in many-body theory: generalities and observables
  • Lehmann representation, spectral weight-function and quasi-particles
  • Perturbative expansion, Feynman diagrams, self-energy
  • Applications: superconductivity
  • Applications: dilute Fermi gas 



A detailed syllabus with references can be found in IOL.

A. L. Fetter, J. D. Walecka, Quantum theory of many-particle systems

W. Nolting, Fundamentals of many-body physics

P. Coleman, Introduction to many body physics

C. Di Castro, R. Raimondi, Statistical mechanics and applications in condensed matter

E. Ercolessi, G. Morandi, F. Napoli - Statistical mechanics: an intermediate course, II edition

S. Sacdhev, Quantum phase transitions

P.M. Chaikin, T.C. Lubensky, Principles of Condensed Matter Physics

J.K. Asboth, L. Oroszany, A. Palyi, A short course on topological insulators

B.A. Bernevig, Topological Insulators and Topological Superconductors

Teaching methods

The course consists of about 48 hours of class lectures, given by the teachers at the blackboard and/or with slides.

Assessment methods

Oral exam: students are asked to prepare a seminar on some topic of interest, which has to be agreed with the teachers.

A list of possible topics can be found in IOL.

Students should demonstrate to be familiar and have a good understanding of the different sujects.

They will be asked to both present an introduction to the main general topics and to prove more specific results, making connections among the different parts of the syllabus.

The organization of the presentation and a rigorous scientific language will be also considered for the formulation of the final grade.

The “cum laude” honor is granted to students who demonstrate a personal and critical rethinking of the subject.

According to the general rules of the University, students will be allowed to reject the grade only once, but they can withdraw at any time during the exam.

Teaching tools

Notes and slides, available to download from the university repository

Office hours

See the website of Elisa Ercolessi

See the website of Pierbiagio Pieri