OVERVIEW

The lectures provide an overview of the effects of topology in condensed matter systems

AIMS AND CONTENT

LEARNING OUTCOMES

The lectures aim at providing the tools for a theoretical understanding of the effects of topology in condensed matter physics. The main aim is to address topological phase transitions in fermionic and spin systems.

AIMS AND LEARNING OUTCOMES

At the end of this teaching, the student will be able to:

1. Describe the basic concepts related to interactions in many-body systems.
2. Apply perturbative approach tools to problems with multiple energy scales.
3. Calculate the topological properties of band models.
4. Use symbolic computing tools (such as Mathematica software) to manipulate complex expressions and perform analytical calculations.

PREREQUISITES

• FISICA DELLA MATERIA 2 61844
• FISICA TEORICA 61842
• FISICA NUCLEARE, DELLE PARTICELLE E ASTROFISICA 2 61847

TEACHING METHODS

blackboard lectures (online if necessary) where the concepts are explained and, if necerrary, derived. The slides will be used to better describe the relevant experiments.

SYLLABUS/CONTENT

the Hubbadr model,

the Heisenberg model as a limit of the Hubbard model,

Ferromagnetic magnons,

Antiferromagnetic magnons,

The xy model and the quantum phase transitions,

The Kitaev chain and the topological phase transitions,

The Jackiw-Rebbi model,

Thouless pumping,

The quantization ofthe Hall conductance.

RECOMMENDED READING/BIBLIOGRAPHY

SUGGESTED BOOKS * H. Bruus, K. Flensberg, "Many-body Quantum Theory in Condensed Matter Physics" Oxford University Press (2004). * G.F. Giuliani, G. Vignale. "Quantum theory of the electron liquid"". Cambridge University Press (2005). * B. A. Bernevig, T. Hughes, "Topological insulators and topological superconductors". Princeton University Press (2013).

TEACHERS AND EXAM BOARD

Exam Board

NICCOLO' TRAVERSO ZIANI (President)

DARIO FERRARO

FABIO CAVALIERE (President Substitute)

LESSONS

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

Oral exam

ASSESSMENT METHODS

The exam will be held by the teacher and by a second expert in the subject. Its duration is approximately 45 minutes. In the first part of the exam a topic previously chosen by the student is presented. In the second, starting from the presented topic, questions on all parts of the lectures will be asked. 

This method aims at understanding not only the level of understanding, but the communication skills as well and allows to understand in the main aims have been reached. If this is not the case, the student will be encouraged to deepen the understanding, even by asking to the teacher.

Exam schedule

FURTHER INFORMATION

Students who have valid certification of physical or learning disabilities on file with the University and who wish to discuss possible accommodations or other circumstances regarding lectures, coursework and exams, should speak both with the instructor and with Professor Sergio Di Domizio (sergio.didomizio@unige.it), the Department’s disability liaison.