Theory of Frustrated Magnetism
Vorlesung im Vertiefungsgebiet "Theoretische Physik"
Corona
E-Learning resources for the course in OPAL
All course material will be available via OPAL. All participants should sign in via OPAL. Non-university participants can register with OPAL at the log-in screen. OPAL will (hopefully) also offer the possibility for discussions etc. Instructions for exercises will follow.
Lectures/Exercises
Mon, 11:10, BZW/A120
Thu, 11:10, BZW/A120
First lecture Apr 6, 2020
First exercise Apr 16, 2020
Lecure notes
Introduction and Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Problem sheets
Sheet 1 (Apr 6; submit solutions by Apr 14)
Sheet 2 (Apr 23; submit solutions by Apr 30)
Sheet 3 (May 7; submit solutions by May 14)
Sheet 4 (May 28; submit solutions by Jun 4)
Sheet 5 (Jun 15; submit solutions by Jun 22)
Sheet 6 (Jul 6; submit solutions by Jul 13)
Description
Frustrated Magnetism is one of the most active research area of modern condensed matter physics. Frustration refers to a situation where the contributions to the potential energy of a many-many body system cannot be simultaneously minimized, a prime example being a antiferromagnetic Ising model on a triangular lattice. Frustration is the source of many novel phases - in particular novel forms of disorder - and exciting phenomena connected to them, such as quantum number fractionalization. Frustrated magnets can e.g. display spin-liquid phases, with a deep connection to topological states of matter.
The lecture will give an introduction to the field, primarily from a theoretical and conceptual perspective. It will cover general ideas, concrete models for frustrated magnets, theoretical methods such as spin-wave theory, parton constructions, and gauge fields, as well as advanced topics. Relevant experimental observations will be discussed as well.
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 but not required.
Contents
1. Introduction
2. Local moments and microscopic models
3. Spin-wave theory: Collinear vs. non-collinear states
4. Classical degeneracies and order by disorder
5. Spin ice
6. Quantum spin liquids
7. Quenched disorder and glassiness
8. Frustration in metals
(9. Quantum criticality and frustration)
Literature
- H. T. Diep (Ed), Frustrated Spin Systems
- C. Lacroix et al. (Ed), Introduction to Frustrated Magnetism
- S. Sachdev, Quantum Phase Transitions
- A. Auerbach, Interacting Electrons and Quantum Magnetism
- K. Yosida, Theory of Magnetism
- arXive review-style articles: cond-mat/9303014, arXiv:cond-mat/9706153, arXiv:0903.2772, arXiv:1412.8482, arXiv:1601.03742, arXiv:1607.03228, arXiv:1710.04399, arXiv:1711.08455, arXiv:1804.02037, arXiv:1806.10967