Universität Wien

260055 VO Condensed Matter Field Theory (2018W)

2.50 ECTS (2.00 SWS), SPL 26 - Physik
Moodle

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Details

Language: English

Examination dates

Friday 18.01.2019 Monday 04.03.2019

Lecturers

Classes (iCal) - next class is marked with N

Monday 03.12. 09:00 - 12:00 Seminarraum Physik Sensengasse 8 EG
Wednesday 05.12. 09:00 - 12:00 Seminarraum Physik Sensengasse 8 EG
Friday 07.12. 09:00 - 12:00 Seminarraum Physik Sensengasse 8 EG
Monday 10.12. 09:00 - 12:00 Seminarraum Physik Sensengasse 8 EG
Wednesday 12.12. 09:00 - 12:00 Seminarraum Physik Sensengasse 8 EG
Friday 14.12. 09:00 - 12:00 Seminarraum Physik Sensengasse 8 EG
Monday 07.01. 09:00 - 12:00 Seminarraum Physik Sensengasse 8 EG
Wednesday 09.01. 09:00 - 12:00 Seminarraum Physik Sensengasse 8 EG
Friday 11.01. 09:00 - 12:00 Seminarraum Physik Sensengasse 8 EG
Monday 14.01. 09:00 - 12:00 Seminarraum Physik Sensengasse 8 EG
Wednesday 16.01. 09:00 - 12:00 Seminarraum Physik Sensengasse 8 EG
Friday 18.01. 09:00 - 12:00 Seminarraum Physik Sensengasse 8 EG

Information

Aims, contents and method of the course

After a quick review on solid state physics, we start by setting up the second quantization formalism, the language in which many‐body physics is most often discussed. Using this formalism, we derive the second‐quantization Hamiltonian for a simple metal. First, we take into account electron‐electron interactions. Then we introduce the field of lattice vibrations (phonons) and study electron‐phonon interactions to lowest order in perturbation.

Soon, it becomes clear that perturbation expansions become unwieldy and too complicated to handle when one goes to higher orders. That is where Feynman diagrams come into play. We see how the diagrams and the rules to compute them arise for the Hamiltonian of a simple metal. To achieve this, we introduce the concept of a Green’s function and see what information we can extract from this object.
In particular, we discuss the idea of a quasiparticle, and see how this relates to the self‐energy and Dyson resummations.
Once we have introduced at the Feynman graph formalism, we apply it to two textbook cases: it is always useful to have some examples to fall back to when you want to apply the formalism to a new problem. To that end, we study the polaron and we calculate the dielectric function, by evaluating the corresponding Feynman diagrams and doing the appropriate resummations.

Course outcomes

• You are familiar with the second quantization formalism. This includes knowing the difference
between a classical and a quantum field, and being able to rewrite operators from first
quantization to second quantization.

• You know how to find the unperturbed Green’s functions and Feynman rules corresponding to a given Hamiltonian – so you can set up an analyse your own theories for solids.

• You can interpret Green’s functions, and explain the link to quasiparticles.

• You know how to compute higher order Green’s functions using Feynman diagrams, and extract from them properties of the material such as conductivity, optical absorption, bulk modulus,

etc.

Assessment and permitted materials

The course is evaluated through two problem sets, equally weighted in the final grade. The first set tests your knowledge of the second quantization formalism and the basic theory of electrons and phonons.
The second set tests whether you can properly set up Feynman rules and use them to compute physical quantities.

Both sets are estimated to take 25‐30 hours of work. You solve the problem sets individually, and return a report in the form of a scientific work note – something that you would share with colleagues in the lab to explain to them what you did. That means your reports will be evaluated not only on the correctness of the results, but also on your presentation and self‐critical discussion of the results obtained. Stick to the deadline: post‐deadline reports are evaluated, but the grade is halved. You receive feedback on the reports, and in case the report is deemed insufficient to pass, you have a chance to correct it using this feedback.

Minimum requirements and assessment criteria

You need to have had a course on quantum mechanics. Schrodinger equations, Hamiltonians and commutation relations do not scare you. You also know perturbation theory for quantum mechanics. You also need some statistical mechanics, including Fermi‐Dirac and Bose‐Einstein statistics. You also know what a Fermi sphere is and what the Fermi energy is.
A bit of knowledge on solid state physics of course does not harm, but if you do not yet know about phonons or bands, do not worry. You will learn about them (again) in the context of this course.
Finally, you should know some numerical methods. Sadly, many interesting problems do not reduce to easy analytic solutions, and you must be able to use a computer to find the minimum of a function, to find the roots of an equation, and to plot the results as a good quality graph.

Examination topics

Reading list

The course consists of 8 contact moments of 2 hours each. These will be a mix of ex cathedra lectures explaining the course material and exercise sessions with example problems.

Detailed course notes are available in the form of a pdf manuscript.

No textbooks are required, but if you want to learn more and go beyond this introductory course, I recommend these books:

"Condensed Matter Field Theory", Altland and Simons (Cambridge University Press, 2006),
"Solid State Physics, essential concepts", David Snoke (Pearson publishing, 2009).

Association in the course directory

MaG 7, MaG 8, MaG 9, MaG 10, MaG 23, MaG 24

Last modified: Mo 07.09.2020 15:40