F8110 Hands-on Introduction to Electronic Structure and Correlations

Faculty of Science
Spring 2024
Extent and Intensity
1/1/0. 2 credit(s) (plus extra credits for completion). Type of Completion: k (colloquium).
Teacher(s)
doc. Mgr. Jiří Chaloupka, Ph.D. (lecturer)
Jan Kuneš, Ph.D. (lecturer)
Guaranteed by
Jan Kuneš, Ph.D.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: Jan Kuneš, Ph.D.
Supplier department: Department of Condensed Matter Physics – Physics Section – Faculty of Science
Timetable
Mon 19. 2. to Sun 26. 5. Wed 13:00–14:50 Fcom,01034
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Quantum field theory on a lattice is a basic theoretical tool to study electronic correlations in materials. We will introduce the idea of tight-binding model of a periodic solid as well as practical aspects of their one-electron physics. We will introduce the concept of Fock space and second quantization and apply them to small solvable systems. The relationship between physical observables and correlation functions of various operators will be introduced. We will use the 6-site Hubbard model as a pilot problem on which calculations will be performed and concepts demonstrated.
Learning outcomes
At the end of the course students should be able to:
- Compute band structures of tight-binding models on various lattices
- Solve small systems of lattice fermions or spins using exact diagonalization
-Be able to use the linear response theory to analyze various spectroscopic experiments
Syllabus
  • 1. Introduction: lattice models vs continuum description
  • 2. Translation symmetry: Bloch theorem of lattice and in the continuum
  • 3. Lattice models on one-particle level: band structure, density of states, tight-binding representation, folding and unfolding
  • 4. Point group symmetry
  • 5. Band structures of real materials
  • 6. Fock space, second quantization, fermionic sign, fermions vs hard-core bosons (spins)
  • 7. Hubbard molecule: strong coupling (Heitler-London) limit
  • 8. 6-site Hubbard model: spectrum, ground state, weak and strong coupling limit
  • 9. 6-site Hubbard and Heisenberg models: spin-spin correlations (equal time)
  • 10. 6-site Hubbard and Heisenberg models: spin-spin and one-electron correlations (dynamic), spectral function
  • 11. Linear response theory: susceptibilities, correlation functions, elementary derivation
  • 12. 6-site Hubbard model: thermal equilibrium
Teaching methods
Lectures. Interactive tutorials based on Python/Julia notebooks.
Assessment methods
Solution of (2-3) home works is required. Presentation of a final project 15-20 min. The solution of the project typically requires some coding (Python, Julia, Fortran, Mathematica, ...) and about 1-2 days work.
Language of instruction
English
Further comments (probably available only in Czech)
Study Materials
The course is taught once in two years.
General note: L.
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