|SCIENTIFIC DISCIPLINARY SECTOR||FIS/03|
The lectures provide an overview of the effects of topology in condensed matter systems
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.
By the end of the lectures, the students will be able to:
Understand the effects of topology on condensed matter systems,
Know the basics about conductance quantization in quantum Hall systems, Thouless pumping, Jackiw-Rebbi model, and Majorana fermions,
interpret the experimental results about the topological phases of matter
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.
In the first part, the phase transitions are discussed, with particular reference to second order phase transitions. The aspects that will be addressed are
the general picture, as emerging from the Ginzburg-Landau theory,
Spontaneous symmetry breaking and Goldstone modes,
The exact solution of the one-dimensional Ising model,
The approximate solution of the two-dimensional Ising model, based on the quantum-classical correspondence.
In the second part the following topics will be discussed:
the Hubbadr model,
the Heisenberg model as a limit of the Hubbard model,
The xy model and the quantum phase transitions,
The Kitaev chain and the topological phase transitions,
The Jackiw-Rebbi model,
The quantization ofthe Hall conductance.
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).
Office hours: After the lectures or as agreed between the student and the teacher by email.
NICCOLO' TRAVERSO ZIANI (President)
All class schedules are posted on the EasyAcademy portal.
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.