Master project in the area of Quantum Field Theory and Statistical Mechanics

While often being associated with the study of elementary particles, Quantum Field Theory shares a deep connection with statistical mechanics. The simplest manifestation of this is that the large distance, low energy behaviour of a many body system in the continuum limit is described by a QFT. Many of the breakthrough developments in particle physics were independently achieved in the area of condensed matter physics. Examples include the discovery of asymptotic freedom (Kondo effect), the Higgs mechanism (found in superconductivity) and the renormalization group.

Project Overview

The goal of the project is to use an effective field theory approach to study the large distance behaviour of a certain quantum statistical system -- a one dimensional ‘spin chain’ known as the Heisenberg XXZ model. We’ll be focusing on a regime where the numerics become unreliable. The spin chain turns out to be ‘integrable’. This allows one to apply a powerful array of methods and describe the low energy spectrum at large system size analytically.

We believe it is detrimental to the student to overspecialize in a narrow topic at the masters stage of their career. As such, the project has been designed to allow the student to gain an understanding of concepts that are important to many disciplines in theoretical physics, e.g., perturbation theory, the renormalization group and effective field theory. The candidate will benefit from close interactions with Dr. Gleb Kotousov, while broad oversight will be provided by Prof. Holger Frahm. The project may result in a publication.

Requirements

The student is expected to have a solid background in applied mathematics and be able to use or learn a basic computer language for numerical work. A good understanding of quantum mechanics is also required. If the student does not have some familiarity in quantum field theory already, it would be ideal for them to take the quantum field theory course offered in the 2024/25 winter semester at the department.

About the group

Prof. Frahm’s research lies at the interface of condensed matter theory, quantum field theory and mathematics. He studies so-called ‘integrable’, low dimensional models to gain insights into the
collective behaviour of correlated many body systems.

For more information please contact Prof. Holger Frahm or Dr. Gleb A. Kotousov.