Lecture 1:
Introduction to Tensor Networks for Classical and Quantum Systems

I will introduce the idea of a tensor network and show how they can be used as a powerful tool to study many-body physics (both classical and quantum). We will begin with a quick survey of the graphical language, which is a convenient tool for describing complicated systems of many particles. We will then apply this graphical language to the classical setting and demonstrate how they exactly relate to classical thermal states. One can easily extend this to stochastic evolution as well as both real- and imaginary-time evolution of quantum systems. We will conclude with a basic introduction of how to calculate wavefunctions and expectation values in many-body quantum systems, which lead to deep implications on the entanglement structure of “typical” many-body wavefunctions.

Tuesday, November 25, 2014, 10:15. Blue Lecture Room


Lecture 2:
Using Tensor Networks with Julia

In this lecture I will go into more detail into some common algorithms that use tensor networks, and demonstrate their use in real-time by programming in a new scientific programming language called “Julia” (http://julialang.org). Julia is a free, high-level technical computing language released in 2012 that combines the speed and simplicity of programming in MATLAB, the performance of C/Fortran, and the extensibility of C++/Python/Lisp. The class will serve as a tutorial introduction to Julia while allowing us to program some simple (yet powerful) tensor network algorithms as examples. Participants are encouraged (but not required) to bring a laptop along to learn and practice - Julia is easy to install on Windows, Mac or Linux. Apart from learning more about tensor networks, you may find that Julia can become a productive tool for your research.

Tuesday, December 2, 2014, 10:15. Blue Lecture Room