Physics Department, TUM | Module PH2310

Basic Information

PH2310 is a semester module in English language at Master’s level which is offered in summer semester.

This Module is included in the following catalogues within the study programs in physics.

Specific catalogue of special courses for condensed matter physics
Focus Area Theoretical Quantum Science & Technology in M.Sc. Quantum Science & Technology
Complementary catalogue of special courses for nuclear, particle, and astrophysics
Complementary catalogue of special courses for Biophysics
Complementary catalogue of special courses for Applied and Engineering Physics
Specialization Modules in Elite-Master Program Theoretical and Mathematical Physics (TMP)

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workload	Contact hours	Credits (ECTS)
300 h	90 h	10 CP

Responsible coordinator of the module PH2310 is Johannes Knolle.

Content, Learning Outcome and Preconditions

Content

Magnetism has been known for millennia but a microscopic understanding has only emerged with the advent of Quantum Mechanics in the last century. This module introduces the basic concepts of quantum magnetism and the theoretical description of magnetic quantum phases of matter. Apart from foundational concepts for long-range ordered ferro- and antiferro-magnetic phases, the lecture covers latest developments in the description of strongly correlated quantum magnets, for example spin fractionalization in quantum spin liquids.

The following topics will be covered in the module:

Magnetic moments and exchange interactions

Types of magnetic order and spin waves

Topological magnon insulators

Magnetism in metals

The Hubbard model: Stoner FM and spin density wave AFM

Kondo effect, heavy fermions and Doniach's phase diagram

Frustrated Magnetism

Classical and quantum order by disorder

Quantum spin liquids and Fractionalization

Kitaev spin liquids and candidate materials

Learning Outcome

After successful completion of the module the students are able to...

...know and classify different types of magnetism

...perform spin wave calculations and calculate spin structure factors

...understand the different contributions to the magnetic response of metals

...perform calculations for the FM and AFM phases of the Hubbard model

...understand the origin of magnetic frustration, non-bipartite lattices and competing interactions

...understand quantum order by disorder

...perform parton mean field calculation for describing quantum spin liquids

...know the origin of spin fractionalization and its experimental consequences

...understand the Majorana fermion solution of Kitaev models

...know about candidate materials and experimental signatures of quantum magnets

Preconditions

In addition to the requirements for the Master’s program in Physics an understanding of second quantization and quantum statistical mechanics is needed.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

SS 2021

Type	SWS	Title	Lecturer(s)	Dates	Links
VO	4	Quantum Magnetism	Knolle, J.	Tue, 08:00–10:00, virtuell Fri, 10:00–12:00, virtuell	eLearning
UE	2	Exercise to Quantum Magnetism	Jin, H. Sim, G. Willsher, J. Responsible/Coordination: Knolle, J.

Learning and Teaching Methods

The main topics and theoretical tools are presented in the lectures, usually in a blackboard style presentation. The application of basic methods and additional specialised techniques are covered in the tutorials. The homework problems are designed to develop the analytic skills of the students and it is expected that solutions are presented and discussed in the tutorial classes.

Media

Blackboard lectures, written notes for download, exercise sheets

Literature

The following books and advanced reviews will be used:

A. Auerbach: Interacting Electrons and Quantum Magnetism

P. Fazekas: Lecture Notes on Electron Correlation and Magnetism

S. Blundell: Magnetism in Condensed Matter

P. Coleman: Introduction to Many-Body Physics

H.T. Diep (Ed.): Frustrated Spin Systems

C. Lacroix et al. (Eds.): Introduction to Frustrated Magnetism

X.-G. Wen: Quantum Field Theory of Many-Body Systems

Knolle and Moessner: A Field Guide to Spin Liquids

Savary and Balents: Quantum Spin Liquids

Module Exam

Description of exams and course work

There will be an oral exam of 30 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions and sample calculations.

For example an assignment in the exam might be:

Explain the basics of parton descriptions of quantum spin liquids and its relation to spin fractionalization
Explain the basic idea for quantum order by disorder and how to treat it microscopically
Explain the SDW phase of the half filled Hubbard model and its excitations

Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.

Exam Repetition

The exam may be repeated at the end of the semester.

Current exam dates

Currently TUMonline lists the following exam dates. In addition to the general information above please refer to the current information given during the course.

Title
Time	Location	Info	Registration
Exam to Quantum Magnetism
Tue, 2021-09-28		Dummy-Termin. Wenden Sie sich zur individuellen Terminvereinbarung an die/den Prüfer(in). Anmeldung für Prüfungstermin zwischen Di, 28.09.2021 und Sa, 23.10.2021. Melden Sie sich bitte nur an, wenn Sie die Prüfung verbindlich auch nach Lektüre der Informationen unter https://www.tum.de/die-tum/aktuelles/coronavirus/pruefungen/ ablegen werden. // Dummy date. Contact examiner for individual appointment. Registration for exam date between Tue, 2021-09-28 and Sat, 2021-10-23. See https://www.tum.de/en/about-tum/news/coronavirus/coronavirus-exams/ for further information and only register after reading!	till 2021-09-27