Statistical Quantum Field Theory 2

A.Y. 2023/2024
6
Max ECTS
42
Overall hours
SSD
FIS/02
Language
Italian
Learning objectives
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.
Single course

This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.

Course syllabus and organization

Single session

Lesson period
Second semester
Course syllabus
Definition of Quantum Phase Transition

Quantum antiferromagnets, Heisenberg spin chains XX, XY, XXZ and XYZ

Jordan-Wigner representation; the exact solutions of the XX and XY model.

The XXZ and the Luttinger model

The exact solution of the Luttinger model. Bosonization and anomalous commutator. Haldane Luttinger liquids

The Ashkin Teller and the eight vertex model; mapping in coupled ising models.

Renormalization Group for system with non trival fixed points,
The phi^4 model in 3 dimension and the epsilo expansion; computation of crtitical exponents at the critical point

Renormalization Group for system with vanishing beta function: interacting fermions in 1d. Ward Identies and Schwoinger-Dyson equation

Graphene, Haldane model and topological insulator. Emerging Firac fermions and Renormalization Group
Prerequisites for admission
Basic Notions of quantum and statistical mechanics
Teaching methods
Lectures in class
Teaching Resources
C. itzykson, J. Drouffe Statistical Field Theory, Cambridge Un. Press 1991
G. Parisi Statistical Field Theory
Fradkin Field Theories of condensed matter physics Cambridge Un. Press 1991
V. Mastropietro Non perturbative Renormalization
Assessment methods and Criteria
Oral and written exam
FIS/02 - THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS - University credits: 6
Lessons: 42 hours
Professor: Mastropietro Vieri
Educational website(s)