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Tensor Networks 2021 – Tutorials

Tutorials

Tutorial Date Materials updated Topic
T16 20.07.21 T16 MPS-based machine learning (optional)
T15 13.07.21 T15 GILT, FET
1. Graph-independent local truncation (GILT)
2. Full environment truncation (FET)
T14 06.07.21 T14 TRG, Simple update
1. Tensor renormalization group to compute correlation functions
2. Simple update to find ground states
T13 29.06.21 T13 Finite PEPS
1. RVB state & Toric code & Resonating AKLT loop state
T12 22.06.21 T12.1
T12.2
T12.1b
T12.2b
NRG II
1. Thermodynamic properties
2. Spectral function
T11 15.06.21 T11
T11b
NRG I
1. Iterative diagonalization & Energy flow diagram
T10 08.06.21 T10.1
T10.2
T10.3
T10.4
Finite temperature. TDVP. QSpace tDMRG (optional)
1a. Purification
1b. XTRG (optional)
2. TDVP
3. Error estimation
4. QSpace tDMRG (optional)
T09 01.06.21 T09.1
T09.2
tDMRG/Subspace expansion
1. tDMRG. XY chain - domain wall. Entanglement growth. Error analysis. Local excitation.
2. Subspace expansion.
T08 25.05.21 T08.1
T08.2
iTEBD. QSpace DMRG (optional)
1. Ground state search. Hastings' method. Correlation length of spin-1 Heisenberg chain. Orthogonalization
2. QSpace: ground state DMRG (optional)
T07 19.05.21 T07.1
T07.2
DMRG
1. Ground state search. Spin-spin correlator. 1st excited state search. Majumdar-Gosh Model
2. Two-site DMRG
T06 18.05.21 T06.1
T06.2
QSpace II
1. Iterative diagonalization (optional)
2. Canonical form (optional)
T05 11.05.21 T05.1 QSpace
1. Introduction to QSpace
2. Iterative diagonalization (optional)
3. Canonical form (optional)
T04 04.05.21 T04.1
T04.2
T04.3
AKLT model, MPOs
1. Left-normalization
Transfer operator
Spin transfer operators
Spin correlators, string order parameter
2. Applying MPO to MPS
3. Parton treatment of Haldane-Shastry model
T03 27.04.21 T03.1
T03.2
T03.3
MPS, Iterative diagonalization
1. Canonical forms of MPS
2. Expectation values
3. Iterative diagonalization of fermionic chain
T02 20.04.21 T02.1
T02.2
T02.3
Tensor network basics
1. Tensor contraction
2. Singular value decomposition
3. Tensor decomposition and entanglement Entropy
T01 15.04.21 T01 MATLAB 101
Introduction to MATLAB

During tutorial sessions, you will learn how to write and use MATLAB codes for tensor network methods.
In the first week of the semester, lectures will be on Tuesday and Wednesday, and the tutorial on Thursday.
In all other weeks of the semester, the tutorial will be on Tuesday, and lectures on Wednesday and Thursday.

Getting started: Read Organization of tutorials, then read readme.pdf and follow the instructions therein about the code repository.

Organization of tutorials
Code repository
Grading rules

Tutorial materials:
Please download the tutorial material on a weekly basis from the links below.