A smal lecture series: “A Brief Introduction to Tensor Networks and Their Applications in Numerical Methods” (lecture 1)

A smal lecture series: “A Brief Introduction to Tensor Networks and Their Applications in Numerical Methods” (lecture 1)

A smal lecture series: “A Brief Introduction to Tensor Networks and Their Applications in Numerical Methods” (lecture 1)

by Ryan Sweke

Title: A Brief Introduction to Tensor Networks and Their Applications in Numerical Methods

Over the last 15 years tensor network representations of many body quantum states have emerged as powerful theoretical and numerical tools in the study of many body and condensed matter physics. In these talks I will provide a brief introduction to and motivation of tensor networks, focusing particularly on one dimensional systems (i.e. Matrix Product States) and their application to the formulation of numerical methods such as DMRG (Density Matrix Renormalisation Group) and TEBD (Time Evolving Block Decimation).

Lecture 1: (a) Introduction and motivation of tensor networks, with particular focus on Matrix Product States (MPS) and Matrix Product Operators (MPO) for one-dimensional systems.

(b) The foundations of numerical analysis with Matrix Product states – i.e. Canonical Forms, Calculation of observables and overlaps, MPO representations of Hamiltonians.

Lecture 2: (a) DMRG in the language of MPS – an efficient algorithm for finding the ground state of gapped one-dimensional Hamiltonians.

(b) TEBD an efficient algorithm for the time evolution of nearest-neighbour Hamiltonians in one-dimension