Topics may include:

• Overview of phase transitions in interacting quantum many-body systems (metal-insulator transition, magnetism, superconductivity)
• Spontaneous symmetry breaking and associated collective (Goldstone) modes
• Classification of phase transitions, the notion of critical exponent, and the experimental evidence for universality
• Ising ferromagnet, and its description in terms of ϕ4-theory
• Mean-field theory for ϕ4-theory. Landau-criterion. Upper and lower critical dimensions
• Idea of renormalisation. Block-spin renormalisation in 1D, and the absence of a transition
• The notion of relevant and irrelevant operators
• Perturbative Wilsonian renormalisation group in d = 4 − epsilon dimensions for ϕ4-theory. Predictions for critical exponents

Learning outcomes

By the end of the module, you will be able to:

• Understand and apply techniques to interacting quantum many-body systems at finite temperatures (Green’s functions/Feynman diagrams)
• Formulate many-body statistical mechanics in terms of functional integrals and second quantization
• Apply a systematic understanding of mean-field theory, upper- and lower-critical dimension to relevant systems
• Identify and demonstrate the idea of universality, i.e. why the same mathematical theories describe a wide range of physical systems
• Perform the simplest Wilsonian renormalisation group calculations (e.g. blockspin or ϕ4)
• Identify and apply the most relevant tools introduced in the module to unfamiliar systems, analysing the potential and limitations of such tools.

​​T​he standard entry requirements comprise:

• A 2:2 honours degree or international equivalent in Physics: Statistical mechanics, quantum mechanics plus condensed matter
• A CV and personal statement outlining your reasons for study
• English language band D (for example, IELTS 6.5 overall with a minimum of 6.0 in each skill).
• Recommended: Modelling Quantum Many-body Systems (7CCPNE05; 1st semester)

Assessment

You will be assessed via an examination and coursework.

This is an on-campus module. Lectures will be held on a single day of the week, each week, during term time. You will be expected to be on-campus for these. Exact dates and times will be confirmed upon enrolment.