Plans for week 38, September 19-23

Welcome back  to you all.
Last week we summarized our discussions on Wick's theorem, with a discussion of what is called the generalized Wick's theorem as well. Thereafter we moved over to a diagrammatic representation.
We worked also on an exercise based on a simplified model called the Lipkin model. This model will follow us in this course as it allows us to illustrate many important aspects of many-body theories. We will encounter it again when we discuss full configuration interaction theory, Hartree-Fock theory and other many-body theories. Lately it has been used in applications of algorithms for quantum computing as well.
The exercises for this week contain a follow-up exercise based on the Lipkin model from last week. Feel free to continue working on the Lipkin model this week as well, in addition to the two other exercises this week, see 
https://github.com/ManyBodyPhysics/FYS4480/blob/master/doc/Exercises/2022/ExercisesWeek38.pdf
This week we will focus on the particle-hole formalism mainly, with examples and the introduction of a new vacuum reference state and normal-ordered operators with respect to the new vacuum reference state.
If we get time we will also discuss how to rewrite creation and annihilation in terms of Pauli matrices (used in quantum computing).  The slides this week are at https://manybodyphysics.github.io/FYS4480/doc/web/course.html, just scroll down to week 38.

The plans for this week are thus
Topics to be covered
Thursday: Discussion of particle-hole formalism with examples
Friday: Particle-hole formalism and definition of new reference state, normalordering of operators. Work on exercise set for week 38.

Lecture Material: Slides for week 38, handwritten notes and chapter 3 and 4 of Shavitt and Bartlett covers most of the material discussed this week.
Fourth exercise set at https://github.com/ManyBodyPhysics/FYS4480/blob/master/doc/Exercises/2022/ExercisesWeek38.pdf

Best wishes to you all,
Morten and ?yvind