lecturer: Prof. Kun Chen

• Course Title: Effective Field Theory of the Many-Electron Problem

• Course Description: This course provides a comprehensive introduction to effective field theory (EFT) and its applications in the many-electron problem. Through a series of focused daily sessions, participants will embark on a journey starting from the fundamental principles of EFT and progressing to its practical applications in various domains, including the precise computation of many-electron correlations and first-principle studies of real materials. The course aims to equip participants with a deep understanding of EFT and its role in advancing electronic structure theory.

• Prerequisites:

Familiarity with quantum mechanics

Basic understanding of Feynman diagrams, Green's functions, and many-body physics

• Reference(s):

"Quantum Theory of the Electron Liquid" by G. Vignale

"Interacting Electrons" by R. Martin, L. Reining, and D. Ceperley

"Effective Field Theory and the Fermi Surface" by Joseph Polchinski

• Schedule:

Day 1 (Jan. 13):

10:00-11:00 & 11:20-12:20: Fundamentals of Effective Field Theory

Introduction to EFT, Power counting, renormalization, and renormalization group methods, EFT perspective on the Ginzburg-Landau framework for many-body systems

Day 2 (Jan. 14):

10:00-11:00 & 11:20-12:20: Effective Field Theory of the Fermi Liquid

Landau Fermi liquid theory, Structure of effective electron-electron interaction, EFT perspectives on the Fermi Gas, Fermi liquid, and the Electron Liquid, 

Day 3 (Jan. 15):

10:00-11:00 & 11:20-12:20: Computing Many-Electron Correlations with EFT

Field-theoretical approaches to the electron gas problem, Numerical algorithms for computing Feynman diagrams based on the AI tech stack, Computing many-electron correlation functions using numerical EFT,

Day 4 (Jan. 16):

10:00-11:00 & 11:20-12:20: EFT Perspective on Ab-Initio Methods

Structure of many-electron correlations, Origin of the local density approximation, EFT perspective on density functional theory and the GW approximation, 

Day 5 (Jan. 17):

10:00-11:00 & 11:20-12:20: Application of EFT in First-Principle Calculations

EFT analysis of Lithium metal, EFT approach to electron-phonon interactions and conventional superconductivity, Summary and Future Directions