Teaching plan for the course unit



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General information


Course unit name: Condensed Matter Physics

Course unit code: 574635

Academic year: 2021-2022

Coordinator: Maria Moreno Cardoner

Department: Department of Quantum Physics and Astrophysics

Credits: 6

Single program: S



Estimated learning time

Total number of hours 150


Face-to-face and/or online activities



-  Lecture





-  Lecture with practical component




Independent learning






Students are advised to have a solid background on the subjects of Quantum Mechanics, Statistical Physics and Solid State Physics. Knowledge on Many-Body Quantum Mechanics and Ultracold Systems is also recommende



Competences to be gained during study


Capacity for theoretical modelling: identify the essence of a process and adopt the correct approaches for reducing a problem to a manageable scale.





Learning objectives


Referring to knowledge

  1. To acquire a general overview on several topics of condensed-matter physics that are relevant for quantum technologies.  

  2. To learn and apply basic concepts and tools for the description of  many-body quantum phenomena in the weakly and strongly interacting regimes. 

  3. To become familiar with recent experimental implementations of condensed-matter models and related phenomena. 



Teaching blocks


1. Basic Concepts


  1. Overview of Condensed-Matter Physics 

  2. Crystalline Structure 

  3. Phonons

  4. Electrons in Solids: Drude model, free electron gas in a periodic potential, Bloch and Floquet theorems, Landau Fermi liquid theory

  5. Phase transitions: Landau theory, order parameter, spontaneous symmetry breaking, Mermin-Wagner theorem

2. Weakly Correlated Systems


  1. (reminder) Non-interacting systems of bosons. Bose-Einstein condensation (off-diagonal order, effects of temperature and finite trapping, experimental observation).

  2. Weakly interacting bosonic gas: Gross-Pitaevskii equation. Bogoliubov theory. Lee-Huang-Yang correction

  3. Weakly interacting fermionic gas: Normal and superfluid fermi gas. Cooper pairs and BCS theory

  4. Superfluidity and Superconductivity. Landau criterium

  5. Low dimensional quantum gases: (1D) Luttinger liquids, bosonization, spin-charge separation. (2D) BKT theory.

3. Strongly Correlated Systems


  1. Tight-binding method. Wannier functions. Spin exchange and superexchange processes. Microscopic derivation of the Hubbard model. Mott-insulating states.

  2. Strong coupling regime: the t-J and Heisenberg models.  

  3. Quantum magnetism: Ferromagnetic and Antiferromagnetic ground states. Spin-wave excitations. Lieb-Schultz-Mattis theorem. Valence bond solids and spin liquids. 

4. Transport phenomena


  1. Semiclassical theory of transport. Boltzmann equation. Linear response theory. 

  2. Anderson localization. Scaling theory.

  3. Quantum dynamics in strong magnetic fields and integer quantum Hall effect.



Teaching methods and general organization


  1. Lectures where theoretical contents of the subject are presented. 

  2. Practical exercise classes in which students are asked to participate. 

  3. Activities related to the subject suggested by the teaching staff. 



Official assessment of learning outcomes


  1. Weekly hand-in of specified homeworks. 

  2. A final written examination on the entire course content worth 6 points. 

  3. Members of the teaching staff may also consider students’ participation in class and in the optional tasks they suggest. Evaluation of competences



Reading and study resources

Consulteu la disponibilitat a CERCABIB


Steven H. Simon “The Oxford Solid State Basics”, Oxford University Press (2013).

L. D. Landau and E. M. Lifschitz, "Statistical Physics (part 2) Vol.9" Pergamon, (1980). 

L. P. Pitaevskii and S. Stringari, "Bose-Einstein condensation", Oxford: Clarendon Press (2003).

M. Lewenstein, A. Sanpera and V. Ahufinger, "Ultracold Atoms in Optical Lattices: Simulating Many-Body Systems", Oxford University Press (2012). 

S. M. Girvin and K. Yang, "Modern Condensed Matter Physics", Cambridge University Press (2019). 

A. Auerbach, "Interacting Electrons and Quantum Magnetism", Springer-Verlag NY (1994). 

S. Sachdev, Quantum Phase Transitions, Cambridge University Press (1999).

Web page

  1. S. Giorgini, “Lecture Notes on Statistical Mechanics” - Course for the Master degree in Physics at the University of Trento


Steven H. Simon “The Oxford Solid State Basics” Oxford University Press, 2013

Book draft http://www-thphys.physics.ox.ac.uk/people/SteveSimon/condmat2012/LectureNotes2012.pdf