[s25] Machine learning for quantum systems (Bohrdt)

[s25] Introduction to Sachdev-Ye-Kitaev (SYK) models

This course provides an in-depth exploration of SYK-type models as a framework for understanding non-Fermi liquid behavior in strongly correlated quantum systems. These models have become synonymous with self-averaging many body systems. Starting with the breakdown of Fermi liquid theory, the course motivates the need for alternative approaches to describe such systems. Designed for advanced students with prior knowledge of second quantization and path integral formalism, the course emphasizes the mathematical structure and physical insights of SYK models, primarily using path integral techniques.

Key topics include:
1. Breakdown of Fermi Liquid Theory
• Overview of Fermi liquid theory.
• Key experimental and theoretical challenges in strongly correlated systems.
• Motivation for SYK-type models as a new framework.
2. Foundations of Path Integrals
• Review of standard path integrals and their applications.
• Grassmann path integrals for fermionic systems.
• Spin coherent state path integrals for spin systems.
3. SYK Model Framework
• Self-averaging and quenched disorder.
• Keldysh contours and their role in nonequilibrium dynamics.
• Derivation and analysis of the Kadanoff-Baym equations.
• Thermodynamics and spectral properties of SYK models.

The course includes weekly 2-hour lectures, complemented by discussions on recent research developments. By the end of the course, students will develop a robust understanding of the path integral formulation of SYK models and their application to modern quantum systems.