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
Outline:
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
Literature:
- An introduction to integrable techniques for one-dimensional quantum systems, F. Franchini arxiv.org/abs/1609.02100
- 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