The most interesting and difficult problems in physics are strongly correlated systems, where emergent phenomena arise that appear fundamentally different from their constituent pieces. This course will focus on how we can better understand strongly correlated phenomena from an algorithmic perspective. This includes both learning the computational methods used to simulate quantum systems as well as understanding how an algorithmic perspective, such as tensor networks, have given us a new way to think about strongly correlated physics. Algorithms that will be covered include the density matrix renormalization group, tensor networks, quantum Monte Carlo, and dynamical mean field theory. Physics examples will include area laws (we will cover the proof that entanglement is bounded in 1D gapped systems); a perspective on ADS/CFT via quantum error correcting codes and perfect tensors; understanding how the sign structure influences the physics of systems; and quantum computing.
Although there are no official prerequisites for this course, the course will be heavy on computational methods and require a willingness to program non-trivially.
This course will be challenging and is designed to push you to the edge of the research frontier and so, in many cases, will cover bleeding edge approaches, applications, and current research - you will be expected to read certain relevant papers and participate in discussing them.
The key to this class will be homework. This is the aspect of the course you will learn the most from. It will often involve programming and is designed to teach you important concepts in simulating quantum systems. There will be four broad classes of homework.
Standard Problem Sets (4-6): Must be done by yourself. ~50% of the grade
The class will develop a set of computational methods based around each lecture which will be posted on the website. You are responsible for one computational module that is based around one lecture ( ~15% of the grade). This means you can do all the work on one module,1/2 the work of two modules, 1/N the work of N modules. Multiple people can't separately get full credit for the same work. See below for coordination.
Final Project ~25% of the grade
A comment about partial credit: There will not be significant partial credit for code that doesn't produce the correct answer There are a million ways a code can be incorrect and it's very hard to evaluate how close you were to the correct answer. On the other hand, you should be able to tell if your homework is correct before submitting. (this is an important skill to develop!)
Homework Submissions: Please submit through the Box.com upload folder HW_Submissions_AlgorithmicPerspective... (preferable) or through the piazza site (less preferable).
Late Homework: Please hand homework in on time. If you get behind, it will be hard to catch up. There will be a penalty for sufficiently late homework.
Questions about grading: If you have a question about the grading of homework, please first see the grader. If you are still unhappy with the resolution, come talk to me.
Solutions: The solutions will be generated by some linear combination of your homeworks and our solutions.
(currently under construction)
Problem Set 1 (Due: September 14 )
Problem Set 2 (Due: October 8 )
Problem Set 3 (ijulia notebook)(Due: November 3 )
Problem Set 4 (Due: December 2 )