- Docente: Pierbiagio Pieri
- Credits: 6
- SSD: FIS/02
- Language: English
- Moduli: Pierbiagio Pieri (Modulo 1) Cristian Degli Esposti Boschi (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Physics (cod. 9245)
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from Sep 30, 2022 to Dec 23, 2022
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from Oct 03, 2022 to Nov 14, 2022
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
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
Readings/Bibliography
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
M. Henkel, Conformal Invariance and Critical Phenomena
A. Auerbach, Interacting Electrons and Quantum Magnetism
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 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
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
Office hours
See the website of Pierbiagio Pieri
See the website of Cristian Degli Esposti Boschi