Statistical Quantum Field Theory 2
A.Y. 2023/2024
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.
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.
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: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
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
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
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)