Strongly Interacting Electrons

From Quantum Dots to High-Temperature Superconductivity

Lectures/Exercises

Mon, 11:10, BZW/A120
Thu, 13:00, BZW/A120

First lecture Apr 13, 2015
First exercise Apr 23, 2015

Exercise sheets

Problem set 1 (Discussion Thu Apr 23)
Problem set 2 (Discussion Mon May 4)
Problem set 3 (Discussion Mon May 18)
Problem set 4 (Discussion Mon Jun 8)
Problem set 5 (Discussion Thu Jun 18)
Problem set 6 (Discussion Thu Jul 2)
Problem set 7 (Discussion Thu Jul 16)

Description

Strongly interacting electrons constitute one of the central research areas of modern condensed matter physics. Starting from the discovery of high-temperature superconductivity in 1986, ideas from this field have penetrated and inspired almost all branches of solid-state research and have led to an amazing development of both experimental techniques and theoretical ideas. The rich physics of correlated systems includes novel states of matter like unconventional superconductors, Mott insulators, fractional quantum Hall states, and spin liquids with excitations carrying fractional quantum numbers as well as technologically important effects like colossal magnetoresistance and multiferroic behavior.

The lecture will give an introduction into the theoretical challenges which accompany strong electronic interactions. Models, methods, and phenomena will be discussed, using examples of current research ranging from quantum-dot physics to Mott insulators and high-temperature superconductors.

The lecture is suitable for Master students and PhD students, as well as for Bachelor students who are familiar with second quantization. Basic knowledge in many-particle theory (Green's functions, mean-field theory, diagrammatics) is helpful.

Contents

1. Introduction
2. Models for correlated electrons
3. Local correlations: Kondo effect and quantum dots
4. Mott transition and dynamical mean-field theory
5. Correlations in one dimension: Spin-charge separation
6. High-temperature superconductivity

Literature

• P. Fulde, Electron Correlations in Molecules and Solids
• A. C. Hewson, The Kondo Problem To Heavy Fermions
• S. Sachdev, Quantum Phase Transitions
• N. Nagaosa, Quantum Field Theory in Strongly Correlated Electronic Systems
• T. Giamarchi, Quantum Physics in One Dimensions
   

Supplemental literature on many-body theory

• G. D. Mahan, Many-Particle Physics
• A. Altlands & B. Simons, Condensed-Matter Field Theory