Theory of Frustrated Magnetism
Vorlesung im Vertiefungsgebiet "Theoretische Physik".
Resources in OPAL, including enrollment, are here.
Lectures/Exercises
Mon, 11:10, BZW/A120
Fri, 09:20, BZW/A120
First lecture Apr 3, 2023, additional lecture Thu Apr 6, 2023 at 16:40
First tutorial Apr 17, 2023
Lecure notes
Chapter 1: Introduction and motivation
Chapter 2: Local moments and microscopic models
Chapter 3: Spin-wave theory
Chapter 4: Classical degeneracies and order by disorder
Chapter 5: Spin ice
Chapter 6: Quantum spin liquids
Chapter 7: Frustration in metals
Problem sheets
Problem sets will be given approximately every two weeks and discussed in a subsequent tutorial. You may submit your written solutions beforehand to Bernhard Frank. They will be corrected and graded (each problem has an associated number of points). Bachelor and Master students need to accumulate 25% of the total number of points as part of their specialization module (Bachelor: "Prüfungsleistung", Master: "Prüfungsvorleistung").
Sheet 1 (discussion Apr 17)
Sheet 2 (discussion Apr 28)
Sheet 3 (discussion May 12)
Sheet 4 (discussion May 26)
Sheet 5 (discussion Jun 19)
Sheet 6 (discussion Jul 14)
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. Frustration in metals
8. Quenched disorder and glassiness
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