Cancelled Advanced Condensed Matter Theory

Course content

In this course, we will cover selected topics in condensed matter theory and quantum many-body physics at an advanced and in-depth level.

 Specific topics will vary from year to year. Typical selections will include:

  • Renormalization group for condensed matter systems
  • 1D interacting models, Luttinger liquids and bosonization
  • Overview of the Sine-Gordon model and the BKT phase transition
  • Quantum phase transitions and the Ising model
  • Majorana modes and topological superconductors
  • Berry’s phase
  • Topological insulators
  • Topological order and the toric code
  • Anyons and topological quantum computation
  • Quantum Hall physics

 There are two main objectives for this course:

  1. To complete the preparation of the students interested in pursuing research in the theory of condensed matter, quantum many-body and statistical physics.
  2. To bring students closer to the research activities in this area, by working on selected topics of their choice in the recent literature.

The course will adopt the operator description of many-body physics taught in Advanced Quantum Mechanics and Condensed Matter Theory 1.

The language of field theory will be used as well for some of the topics of this course. The necessary tools from field theory will be discussed during the course, based on either the functional path integral taught in Condensed Matter Theory 2 or the quantum field formulation taught in Quantum Field Theory 1.

Learning outcome


The students will acquire a set of strategies to investigate the physics of complex quantum many-body systems. The course will indeed present several theoretical techniques to describe the main features of a selection of quantum many-body systems of current interest in the scientific community.

In this respect, the students will be invited to think like researchers and describe complex systems by trying different approaches in their analysis.

The training of the students to this kind of research activity will include getting into a new topic by reading original research papers, learning to identify new questions, and distilling key physical principles at play in complex phenomena. In particular, each student will investigate a specific topic, carrying out detailed calculations and writing a final report on his/her understanding and findings.


At the end of the course, the student will know the fundamentals of the year’s selected topics and their connections to other areas of modern physics. The knowledge will be at a level such that the participants will be prepared to follow and conduct research in the given area.


After this course the students will be experienced in a method for starting research in a new area. They will be able to extract the needed information from existing literature and to think about new directions for the research area in question.

The course will present a mixture of lectures, problem sessions and group activities.

Several mandatory assignments are foreseen, including exercise sets and a final report on a topic related to the contents of the course chosen by the student.

To be announced on Absalon.

The student is expected to have passed courses on mathematics, quantum mechanics and statistical physics on the level covered in the corresponding Bachelors courses in Physics at UCPH.

Knowledge of quantum mechanics on the level taught in ”Advanced Quantum Mechanics” at UCPH is required.

Basic knowledge on the main condensed matter physics systems is expected.

Knowledge of quantum field theory or functional path integral is an advantage.

Continuous feedback during the course of the semester

Written feedback will be given about the final report.

7,5 ECTS
Type of assessment
Continuous assessment
Type of assessment details
Written assignments
The evaluation is based on the following homework assignments:
• 3 problems sets (counting for 50% of the final grade)
• Final report (counting for 50% of the final grade)
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners

The format of the re-exam is constituted by a written assignment (one exercise set and a resubmission of the final report, counting for 50% of the final grade in total) and an oral examination (30 minutes without preparation time, counting for 50% of the final grade in total).

Criteria for exam assessment

See learning outcome.

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 40
  • Preparation
  • 122
  • Theory exercises
  • 10
  • Project work
  • 24
  • Guidance
  • 10
  • English
  • 206


Course number
7,5 ECTS
Programme level
Full Degree Master

1 block

Block 4
No restrictions.
The number of seats may be reduced in the late registration period.
Study Board of Physics, Chemistry and Nanoscience
Contracting department
  • The Niels Bohr Institute
Contracting faculty
  • Faculty of Science
Course Coordinator
  • Michele Burrello   (16-4f6b656a676e673064777474676e6e714270646b306d7730666d)
Saved on the 14-12-2023

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Courseinformation of students