• Course Title: Diagrammatic Approaches to Quantum Many-Body Problems

• Prerequisites:

Familiarity with quantum mechanics and statistical mechanics

• Reference(s):

“Quantum Many-particle Systems” by John W. Negele, Henri Orland

“Methods of Quantum Field Theory in Statistical Physics” by A. A. Abrikosov, L. P. Korkov, I. E. Dzyaloshinski

• Schedule:

Day 1 (Jan. 13):

13:30~14:30: Basics of Green’s function method and Feynman diagrams - Part I

Grassmann variables, path integral, Matsubara formalism, Kadanoff-Baym (Keldysh) contour

Day 2 (Jan. 14):

13:30~14:30: Basics of Green’s function method and Feynman diagrams - Part II

Luttinger-ward functional and skeleton (bold) series Multivaluedness problem of Luttinger-Ward functional

Day 3 (Jan. 15):

13:30~14:30: Strong-coupling expansion for quantum impurity model

Strong-coupling expansion and corresponding Feynman diagrams Pseudo-particle theory for quantum impurity model (crossing approximations)

Day 4 (Jan. 16):

13:30~14:30: Computational method for Feynman diagrams - Part I

Quantum monte Carlo, Diagrammatic Monte Carlo, Tensor-train decomposition and tensor-cross interpolation

Day 5 (Jan. 17):

13:30~14:30: Computational method for Feynman diagrams - Part II

Convergent and divergent diagrammatic series, Summary and outlook