87952 - QUANTUM MANY BODY THEORY

Scheda insegnamento

Anno Accademico 2022/2023

Conoscenze e abilità da conseguire

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.

Contenuti

MODULE 1

  • Theory of dilute Bose gases
  • Green’s functions for many-body systems at zero temperature: generalities and observables
  • Lehmann representation, spectral weight-function and quasi-particles
  • Perturbative expansion, Feynman diagrams, self-energy
  • Finite temperature methods: Matsubara formalism
  • Applications: superconductivity

MODULE 2

  • Introduction to quantum phase transitions
  • Lattice models for strongly correlated systems: Hubbard, t-J, and  Heisenberg models
  •  Quantum magnetism, spin chains, Haldane’s gap, and emergence of states with topological properties 

Testi/Bibliografia

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 

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

Metodi didattici

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

Modalità di verifica e valutazione dell'apprendimento

Oral exam: students will be asked to answer three/four questions on different topics covered by the course.

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

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

Orario di ricevimento

Consulta il sito web di Pierbiagio Pieri

Consulta il sito web di Cristian Degli Esposti Boschi