# 138.121 Concepts in Condensed Matter Physics This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_21",{id:"j_id_21",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_23",{id:"j_id_23",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2022W 2021W 2020W 2019W

2022W, VU, 2.0h, 3.0EC

## Properties

• Semester hours: 2.0
• Credits: 3.0
• Type: VU Lecture and Exercise
• Format: Hybrid

## Learning outcomes

After successful completion of the course, students are able to:

1) Identify relevant mathematical structures and concepts in condensed matter problems, e.g. eivenvectors, eigenvalues and other linear algebra structures, correlation functions, inital value and boundary value problem of differential equations, Fourier transform.

2) Use discrete and continuous symmetries to assess the correctness of numerical results and to simplify physical problems

3) Construct Fock space of fermionic problems and apply it to simple systems with few degrees of freedom

4) Use Fourier transforms both in space and time/frequency domain

5) Understand basic approximations used in condensed matter physics, e.g. strong and weak coupling expansion, large-N expansion, embedding, stochastic simulations

6) Calculate magnetic susceptibility of 6-site Hubbard molecule as a function of temperature

## Subject of course

Foundations of quantum theory: causal evolution and measurement, observables, wavefunctions, Hermitean operators, evolution operator and Hamiltonian

Schrodinger equation, stationary states, time evolution, Hemitean and unitary operators

Basic statistical physics, Boltzmann factor

Symmetry and eigenvalue degeneracy

Quantum theory of many particles: fermions and bosons, Pauli principle, commutation relations, Pauli principle

Lattice models, translational symmetry

Exact diagonalization, construction of Fock space and fermionic operators

Correlation functions and linear response to external perturbations

Non-interacting electrons in periodic solids, Bloch theorem

The concepts will be developed step by step on a pilot problem (6-site cluster). We will develop a code to calculate the discussed observables during the coure.

## Teaching methods

`Interactive handling of the course`

## Mode of examination

Oral

The format of the course is in-presence lectures/discussion (recorded lectrues from last year available), individual homework and a computational project at the end.

The language of the course is English.

The 'Vorbesprechung' will take place on October 4, 14:00 @ Sem.R. DB gelb 09

## Course dates

DayTimeDateLocationDescription
Tue14:00 - 15:0004.10.2022Sem.R. DB gelb 09 Concepts in Condensed Matter Physics
Mon13:00 - 15:0007.11.2022 - 23.01.2023Sem.R. DB gelb 09 Concepts in Condensed Matter Physics
Concepts in Condensed Matter Physics - Single appointments
DayDateTimeLocationDescription
Tue04.10.202214:00 - 15:00Sem.R. DB gelb 09 Concepts in Condensed Matter Physics
Mon07.11.202213:00 - 15:00Sem.R. DB gelb 09 Concepts in Condensed Matter Physics
Mon14.11.202213:00 - 15:00Sem.R. DB gelb 09 Concepts in Condensed Matter Physics
Mon21.11.202213:00 - 15:00Sem.R. DB gelb 09 Concepts in Condensed Matter Physics
Mon28.11.202213:00 - 15:00Sem.R. DB gelb 09 Concepts in Condensed Matter Physics
Mon05.12.202213:00 - 15:00Sem.R. DB gelb 09 Concepts in Condensed Matter Physics
Mon12.12.202213:00 - 15:00Sem.R. DB gelb 09 Concepts in Condensed Matter Physics
Mon19.12.202213:00 - 15:00Sem.R. DB gelb 09 Concepts in Condensed Matter Physics
Mon09.01.202313:00 - 15:00Sem.R. DB gelb 09 Concepts in Condensed Matter Physics
Mon16.01.202313:00 - 15:00Sem.R. DB gelb 09 Concepts in Condensed Matter Physics
Mon23.01.202313:00 - 15:00Sem.R. DB gelb 09 Concepts in Condensed Matter Physics

## Examination modalities

Presentation of simple numerical project and discussion of corresponding methods and physical concepts

## Course registration

Begin End Deregistration end
20.09.2022 12:00 10.10.2022 15:00 13.10.2022 12:00

## Curricula

Study CodeSemesterPrecon.Info
066 646 Computational Science and Engineering

## Literature

No lecture notes are available.

## Previous knowledge

basic linear algebra, basic programming

English