# PřF:FK120 Strongly correlated electrons - Course Information

## FK120 Physics of strongly correlated electron systems

**Faculty of Science**

Spring 2025

**Extent and Intensity**- 2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
**Teacher(s)**- doc. Mgr. Jiří Chaloupka, Ph.D. (lecturer)

prof. Mgr. Dominik Munzar, Dr. (lecturer) **Guaranteed by**- prof. Mgr. Dominik Munzar, Dr.

Department of Condensed Matter Physics – Physics Section – Faculty of Science

Contact Person: doc. Mgr. Jiří Chaloupka, Ph.D.

Supplier department: Department of Condensed Matter Physics – Physics Section – Faculty of Science **Course Enrolment Limitations**- The course is offered to students of any study field.
**Course objectives**- Introduction to fundamentals of the theory of strongly correlated electron systems.
**Learning outcomes**- At the end of the course students should understand the physics of simple models of strongly correlated electron systems and they should be able to apply their knowledge in interpreting experimental data.
**Syllabus**- 1. Localised and itinerant electrons in solids.
- 2. (One orbital) Hubbard model.
- 3. Mott transition.
- 4. Selected variational solutions of the problem given by the Hubbard hamiltonian.
- 5. The limit of U>>W, antiferromagnetic Heisenberg hamiltonian and its eigenstates.
- 6. t-J model: renormalisation of holes by the coupling to spin excitations, resonanting valence bond theory.
- 7. Multi-orbital Hubbard model: local correlations, solutons for an isolated ion, multiplet structure.
- Crystal field effects and orbital-dependent inter-site hoppings.
- 8. Spin-orbital models of the Kugel-Khomskii type, Goodenough-Kanamori-Anderson rule.
- 9. Examples from the physics of transition metal oxides.
- 10. Basic ideas of the dynamical mean field theory (DMFT).

**Literature**- D. I. Khomskii: Transition Metal Compounds, Cambridge University Press, Cambridge, 2014
- P. Fazekas: Lecture notes on electron correlation and magnetism, World Scientific, Singapore, 1999
- P. Fulde: Electron correlations in molecules and solids, Springer, Berlin, 1995

**Teaching methods**- Lectures, where the topics are introduced, seminars, where solutions of related problems are presented and discussed.
**Assessment methods**- Exam. The topics of the course, in particular those related to the problems solved by the student, are discussed, in order to assess student's knowledge. The final evaluation reflects the degree of understanding.
**Language of instruction**- Czech

- Enrolment Statistics (Spring 2025, recent)
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