General information 
Course unit name: Condensed Matter Physics
Course unit code: 574635
Academic year: 20212022
Coordinator: Maria Moreno Cardoner
Department: Department of Quantum Physics and Astrophysics
Credits: 6
Single program: S
Estimated learning time 
Total number of hours 150 
Facetoface and/or online activities 
48 
 Lecture 
Facetoface 
32 

 Lecture with practical component 
Facetoface 
16 
Independent learning 
102 
Recommendations 
Students are advised to have a solid background on the subjects of Quantum Mechanics, Statistical Physics and Solid State Physics. Knowledge on ManyBody 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

Teaching blocks 
1. Basic Concepts
*
Overview of CondensedMatter Physics
Crystalline Structure
Phonons
Electrons in Solids: Drude model, free electron gas in a periodic potential, Bloch and Floquet theorems, Landau Fermi liquid theory
Phase transitions: Landau theory, order parameter, spontaneous symmetry breaking, MerminWagner theorem
2. Weakly Correlated Systems
*
(reminder) Noninteracting systems of bosons. BoseEinstein condensation (offdiagonal order, effects of temperature and finite trapping, experimental observation).
Weakly interacting bosonic gas: GrossPitaevskii equation. Bogoliubov theory. LeeHuangYang correction
Weakly interacting fermionic gas: Normal and superfluid fermi gas. Cooper pairs and BCS theory
Superfluidity and Superconductivity. Landau criterium
Low dimensional quantum gases: (1D) Luttinger liquids, bosonization, spincharge separation. (2D) BKT theory.
3. Strongly Correlated Systems
*
Tightbinding method. Wannier functions. Spin exchange and superexchange processes. Microscopic derivation of the Hubbard model. Mottinsulating states.
Strong coupling regime: the tJ and Heisenberg models.
Quantum magnetism: Ferromagnetic and Antiferromagnetic ground states. Spinwave excitations. LiebSchultzMattis theorem. Valence bond solids and spin liquids.
4. Transport phenomena
*
Semiclassical theory of transport. Boltzmann equation. Linear response theory.
Anderson localization. Scaling theory.
Quantum dynamics in strong magnetic fields and integer quantum Hall effect.
Teaching methods and general organization 

Official assessment of learning outcomes 

Reading and study resources 
Consulteu la disponibilitat a CERCABIB
Book
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, "BoseEinstein condensation", Oxford: Clarendon Press (2003).
M. Lewenstein, A. Sanpera and V. Ahufinger, "Ultracold Atoms in Optical Lattices: Simulating ManyBody 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", SpringerVerlag NY (1994).
S. Sachdev, Quantum Phase Transitions, Cambridge University Press (1999).
Web page
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://wwwthphys.physics.ox.ac.uk/people/SteveSimon/condmat2012/LectureNotes2012.pdf
web