Module Description
Besides the solid-liquid-gas trinity of states, quantum matter can realise a cornucopia of phases, such as magnetic states, electronically ordered states, and quantum condensates. This course presents the modern understanding of “phases of matter” and the transitions between them. We will develop and apply concepts and methodologies from statistical / quantum field theory (S/QFT) in the context of many-body physics. The first part of the module will be centred around the “correlated electron problem” and phase transitions in condensed matter—such as metal-insulator, non-magnetic to magnetic, and normal-state to superconducting transitions—introducing, among others, the notion of spontaneous symmetry breaking and the emergence of associated collective (Goldstone) excitations. The more general, second part will formalise critical phenomena and discuss ideas such as universality (why, near criticality, the same description applies to a wide range of systems), introduce aspects of the renormalization group approach, and develop and apply Ginzburg-Landau theory and beyond.
Learning aims & outcomes
1. Understand and apply Green’s function/Feynman diagram techniques to interacting quantum many-body systems at finite temperatures.
2. Ability to identify and describe instabilities of the Fermi liquid.
3. Understand the scaling hypothesis in critical phenomena and the concept of universality.
4. Be able to systematically apply mean-field theory and Ginzburg-Landau theory.
5. Perform the simplest Wilsonian renormalisation group calculations (e.g., block-spin transformation or phi^4).
6. Identify and apply the most relevant tools introduced in the module to unfamiliar systems, analysing the potential and limitations of such tools.
Teaching arrangements
2h lecture, 2h tutorial
Pre-requisites
It is recommended that students taking this course have passed the standard undergraduate courses in linear algebra, quantum mechanics, and statistical mechanics. A definite plus would be the attendance of an introductory course to solid-state/condensed matter physics and the ”Advanced Mathematical Methods for Theoretical Physics” (6CCP9100). The attendance of the first semester course "Modelling Quantum Many-body Systems (7CCPNE05)" is also recommended.
tools.