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TOPOLOGICAL PHASES OF CONDENSED MATTER

CODE 102447
ACADEMIC YEAR 2022/2023
CREDITS
  • 6 cfu during the 2nd year of 9012 FISICA(LM-17) - GENOVA
  • 6 cfu during the 1st year of 9012 FISICA(LM-17) - GENOVA
  • SCIENTIFIC DISCIPLINARY SECTOR FIS/03
    TEACHING LOCATION
  • GENOVA
  • SEMESTER 1° Semester
    TEACHING MATERIALS AULAWEB

    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

    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

    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

    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 phenomenology,

    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,

    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)

    FEDERICO CAGLIERIS

    FABIO CAVALIERE

    DARIO FERRARO

    LESSONS

    Class schedule

    All class schedules are posted on the EasyAcademy portal.

    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.