Fakultät für Physik




Tensor Networks – Tutorials

Notice (22.04.2020): The tutorial material for the course "Tensor Networks 2019" has been taken offline, since a new course has just started: "Tensor Networks 2020". (This course is taught online via Zoom, if you are interested in joining, contact Prof. Jan von Delft.) The tutorial material for "Tensor Networks 2019" can be obtained upon e-mail request to Seung-Sup Lee or Jheng-Wei Li.

During tutorial sessions, students will learn about how to write and use the codes for tensor network methods. Please read and follow the instruction () to start with.

Important notice: On 12.07.2019, exam date and place were assigned to individual students, via e-mail. If you didn't get a mail from us but want to get a grade from this course, please contact Seung-Sup Lee or Jheng-Wei Li as soon as possible.

Code repository: (last updated: 24.07.2019)
The code repository contains functions and scripts commonly used in exercises, while individual exercise materials are uploaded separately below. As the lecture course proceeds, new functions and scripts relevant to the most recently covered topics will be added to the repository. Therefore please update your working directory with the latest version of the code repository on a regular basis.

Exercise materials:
Exercises for each tutorial session will be uploaded two days before the tutorial session. (Minor revisions, such as fixing typos, may occur after the upload.) Please download the exercises from the links below. Then follow the demonstration therein and try to solve exercise problems, before attending tutorial sessions. During tutorial sessions, we will focus on questions and answers, and the discussion on advanced topics. The solutions of the exercise problems will be uploaded after the tutorial session.
Tutorial Date Exercises Solutions Topic
T14 25.07.19

MPS-based machine learning
1. Handwritten digit (MNIST) recognition
(Exercise uploaded: 24.07.2019) (Exercise uploaded: 26.07.2019)
T13 18.07.19

1. Graph-independent local truncation (GILT)
2. Full environment truncation (FET)
(Exercise uploaded: 16.07.2019) (Solution uploaded: 19.07.2019)
T12 11.07.19

TRG, Simple update
1. Tensor renormalization group to compute correlation functions
2. Simple update to find ground states
(Exercise uploaded: 09.07.2019) (Solution uploaded: 16.07.2019)
T11 04.07.19

Finite PEPS
1. Contraction of finite PEPS on a strip
2. RVB state, Toric code, Resonating AKLT loop state
(Exercise uploaded: 02.07.2019) (Solution uploaded: 16.07.2019)

1. Introduction to QSpace library
2. Complete set of local operators
3. NRG iterative diagonalization
(Exercise uploaded: 24.06.2019)
T08 17.06.19

1. tDMRG
2. Entanglement growth, Trotter error
(Exercise uploaded: 14.06.2019) (Solution uploaded: 24.06.2019)
T07 06.06.19

1. Ground state search
2. Hastings' method
3. Correlation function
4. Orthogonalization
(Exercise uploaded: 05.06.2019)
(Solution uploaded: 14.06.2019)
T06 03.06.19

1. Ground state search
2. 1st excited state search
3. Correlation function
(Exercise uploaded: 31.05.2019)
(Solution uploaded: 14.06.2019)
T05 23.05.19

AKLT model
1. Left-normalization
2. Transfer operator
3. Spin transfer operators
4. Spin correlators, string order parameter
T04 16.05.19

T04a. Thermodynamic properties
T04b. Spectral function
(Exercise uploaded: 14.05.2019)
(Exercise T04b revised and solution T04a uploaded: 21.05.2019)
(Solution T04b uploaded: 28.05.2019)
T03 09.05.19

T03a. Iterative diagonalization
T03b. Energy flow diagram
(Exercise uploaded: 07.05.2019)
(Solution uploaded: 14.05.2019)
T02 02.05.19

MPS I: Matrix Product States
T02a. Canonical forms of MPS
T02b. Expectation values
(Exercise uploaded: 30.04.2019)
(Solution uploaded: 07.05.2019)
T01 25.04.19

Tensor Network basics
T01a. MATLAB101
T01b. Tensor contraction
T01c. Singular value decomposition
(Exercise uploaded: 22.04.2019)
(Solution uploaded: 29.04.2019)