Summer Undergrad 2020 - Numerical Methods

This course has two main goals: (1) to introduce some key models from condensed matter physics;  and (2) to introduce some numerical approaches to studying these (and other) models.  As a  precursor to these objectives, we will carefully understand many-body states and operators from  the perspective of condensed matter theory.  (However, I will cover only spin models.  We will not  discuss or use second quantization.)

Once this background is established, we will study the method of exact diagonalization and write  simple python programs to find ground states, correlation functions, energy gaps, and other  properties of the transverse-field Ising model.  We will also discuss the computational limitations  of exact diagonalization.  Finally, I will introduce the concept of matrix product states, and we will  see that these can be used to study ground state properties for much larger systems than can be  studied with exact diagonalization.

Each 90-minute session will include substantial programming exercises in addition to lecture.  Prior programming experience is not expected or required, but I would like everyone to have  python (version 3) installed on their computer prior to the first class, including Jupyter notebooks;  see “Resources” below.