Advanced Methods in Quantum Many-Body Theory (PH2297)

Lecturers: Alvise Bastianello, Wonjune Choi, Hui-Ke Jin, Gibaik Sim (coordination: Johannes Knolle)

Lectures: Mon, Tue 16:00 - 18:00 
Tutorials: Thu 16:00 - 18:00


The course will cover a number of advanced topics in theoretical quantum many-body physics. It will consist of four main parts:

1. Introduction to the thermodynamics and out-of-equilibrium properties of 1d quantum integrable models:

  • The Bose gas and its non-interacting points: the strongly repulsive limit and its fermionization. 
  • Quantum quenches, lack of thermalization and relazation to the Generalized Gibbs Ensemble: the example of the 1d Bose gas.
  • Emergent hydrodynamics in integrable models. 

2. Quantum Spin Liquids: 

  • Introduction to group theory, lattice gauge theory, and projective symmetry group (PSG) theory 
  • Projective construction of quantum spin liquids using PSG. Example: Kitaev honeycomb model. 
  • Beyond mean-field theory: Guztwiller projection. 

3. Phenomenological theory of topological superconductivity: 

  • Short review about BCS theory and pairing order parameters 
  • Group theory 
  • Ginzburg-Landau theory 
  • Gorkov equation and path integral 
  • Topological aspects of superconductivity 

4. Quantum criticality in itinerant magnetic systems: 

  • Short review about critical phenomena and Wilsonian renormalization group 
  • Stoner theory of itinerant magnetism 
  • Wilson-Fisher fixed point of the \phi^4 theory 
  • Hertz-Millis-Moriya theory and its breakdown


  • An introduction to integrable techniques for one-dimensional quantum systems, F. Franchini 
  • Lecture notes on Generalized Hydrodynamics, B. Doyon SciPost Phys. Lect. Notes 18 (2020)
  • Quantum field theory of many-body systems. Xiao-Gang Wen 
  • Anyons in an exactly solved model and beyond. Alexei Kitaev 
  • Quantum orders and symmetric spin liquids. Xiao-Gang Wen 
  • Group Theory and Quantum Mechanics. Michael Tinkham 
  • Physics of projection wavefunctions. Claudius Gros 
  • Introduction to Unconventional Superconductivity, V.P. Mineev and K.V. Samokhin 
  • Introduction to Unconventional Superconductivity, M. Sigrist 
  • Superconducting classes in heavy-fermion systems, G. E. Volovik and L. P. Gorkov 
  • Aspects of Topological Superconductivity, M. Sigrist 
  • Lecture Notes on Electron Correlation and Magnetism, P. Fazekas 
  • Lecture Notes on Electron Correlation and Magnetism, P. Fazekas 
  • Quantum Field Theory in Strongly Correlated Electronic Systems, N. Nagaosa 
  • Condensed Matter Field Theory, A. Altland and B. Simons

TUM Course Website PH2297