# Selected Topics in Modern Condensed-Matter Theory

Prof. Johann Kroha

# Lecture **
physics7503**

Schedule: Wednesdays 14, Fridays 12-14

Room: ATTENTION! The NEW ROOM is

Schedule: Wednesdays 14, Fridays 12-14

Room: ATTENTION! The NEW ROOM is

**Seminarraum 1, BCTP @ Wegelerstr. 10, 2. floor**

(HS I @ PI is currently under construction)

Module description

Module description

**Note:** The topics of this course are coordinated such that it can be taken in parallel to physics617 (Theoretical Condensed Matter Physics).

Prerequisites: Quantum mechanics I, e.g. physik420

Statistical Physics, e.g. physik521

## Contents

Over the past few years, research in condensed matter physics has witnessed several novel developments, which are revolutionizing our understanding of many-body systems. Among those developments are

- the simulation of many-body problems in ultracold atomic-gas systems;
- quantum phase transitions as a means for realizing exotic states of matter;
- topological aspects of Hilbert spaces.

The course will discuss these developments and provide some of the necessary theoretical techniques.

Specific topics are:

- Feynman diagram technique;
- the method of slave fields for strong interactions;
- phase transitions, critical phenomena, renormalization group method;
- topological structure of the Hilbert space and consequences for the properties condensed-matter systems. Topological insulators.

## Literature

- R. D. Mattuck, A Guide to Feynman Diagrams in the Many-Body Problem.
- N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group.
- B. A. Bernevig, Topological Insulators and Topological Superconductors.

## Exercises

## Exams

The exam will take place on Friday, February 10, 2017, 12:00.