Fall 2015 Phys. 598 Course on "Algorithmic Perspective on Strongly Correlated Systems"

Course Information

Professor: Bryan Clark

Meets: Tuesday and Thursday 3:00-4:30 in room Loomis 222

Office hours: TBD

Course Description:  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 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 before lecture and participate in discussing them. There is no good text for this course (there isn’t really even a bad text for this course which covers the material).

Homework: 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 three types of homework. The first will be six standard problem sets that you must complete and submit on your own (though you may discuss with others). They will help you develop your understanding of different computational methods through implementing and reasoning about their subtleties. For the second piece of homework, the class will develop a set of computational methods based around each lecture. Your are responsible for the module for one lecture (or 1/N modules from N lectures). Finally, there will be a final project that will be done in groups.

Course Outline (currently under construction)

1.Introduction

2.Exact Diagonalization

3.Variational Monte Carlo and Wave-functions

4.Projector Monte Carlo 5.World-line Monte Carlo

6.Determinant Monte Carlo

7.Introduction to Tensor Networks

8.DMRG

9.PEPS and MERA

10.Fermion Sign Problem

11.Embedding Techniques

12.Proof of 1D Area Law

13.Quantum Hamiltonian Simulations

14.Perfect Tensors, QEC, and ADS/CFT

15.The algorithmic Frontier