General information 
Course unit name: Tensor Networks
Course unit code: 574645
Academic year: 20212022
Coordinator: Bruno Julia Diaz
Department: Department of Quantum Physics and Astrophysics
Credits: 3
Single program: S
Estimated learning time 
Total number of hours 75 
Facetoface and/or online activities 
26 
 Lecture 
Facetoface and online 
20 

 Lecture with practical component 
Facetoface and online 
6 
Independent learning 
49 
Recommendations 

Competences to be gained during study 

Learning objectives 
Referring to knowledge

Teaching blocks 
1. Generalities
*
An introduction to the tensor network formalism and graphical notation,
Introduction to the tensor network zoo, MPS, PEPS, TTN, MERAs ...
2.
Analytical foundation of tensor networks
*
Matrix product states and their representation
Canonical form and injectivity
Entanglement in manybody quantum systems
The geometry of tensor networks
3.
Tensor networks approaches to statistical mechanics
*
Encoding partition functions
Calculating entropies
4.
Back to quantum systems
*
Transfer matrix and the quantum Hamiltonian
The renormalization group
DMRG as a RG algorithm
5.
Numerical simulation the existing software
*
An overview of the steps in numerical algorithms
Tensor contractions, their cost and strategies
Overview of the main software packages
6.
Numerical simulations building new algorithms
*
Guiding principles
Software libraries helping designing new algorithms
7.
Symmetries in tensor Networks
*
The physical relevance of symmetry
Symmetries in tensor networks
Implementing symmetries in practice
Official assessment of learning outcomes 

Reading and study resources 
Consulteu la disponibilitat a CERCABIB
Book
Video, DVD and film
Topological Matter School. TMS18.L25. Frank Pollmann. Tensor Networks and Matrix Product States (I).; 2018. Accessed January 25, 2021.
ICAM  I2CAM. Tensor Network States & Entanglement Renormalization I  Verstraete.; 2016. Accessed January 25, 2021.
Mini Crash Course: Tensor Networks. Guifre Vidal Accessed February 19, 2020.
Article
J. C. Bridgeman and C. T. Chubb, HandWaving and Interpretive Dance: An Introductory Course on Tensor Networks, J. Phys. A: Math. Theor. 50, 223001 (2017).
Haegeman and F. Verstraete, Diagonalizing Transfer Matrices and Matrix Product Operators: A Medley of Exact and Computational Methods, ArXiv:1611.08519 [CondMat, Physics:MathPh, Physics:QuantPh] (2016).
R. Orus, A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States, Annals of Physics 349, 117 (2014).