Tensor Networks (SS2021)

Vorlesung im Vertiefungsgebiet "Theoretische Physik"

Lectures/tutorials:

Monday & Thursday, 14:50 - 16:20, online via Zoom
First lecture: 12.04.2021 (Monday)

Due to the current situation, this course will be given online via Zoom. For the course enrolment ("Einschreibung") and further instructions, please contact the lecturer by email.

 OPAL course (discussion forum, code sharing)

Information sheet
Course outline (updated on 03.05.2021)

Lecture notes: (videos removed due to Zoom storage limit)

Lecture1 Introduction (12.04.2021)
Lecture2 Real space renormalization (15.04.2021)
Lecture3 Canonical form of MPS (19.04.2021)
Lecture4 Entanglement area law (26.04.2021)
Lecture5 AKLT model (29.04.2021)
Lecture6 MPS injectivity (03.05.2021)
Lecture7 MPO & single-site DMRG (10.05.2021)
Lecture8 Two-site DMRG (17.05.2021)
Lecture9 Fermionic systems (31.05.2021)
Lecture10 MPO-MPS evolution (03.06.2021)
Lecture11 Trotter-Suzuki decomposition (07.06.2021)
Lecture12 Time-evolving block decimation (14.06.2021)
Lecture13 Real- and imaginary-time evolutions (17.06.2021)
Lecture14 Symmetry in MPS (21.06.2021)
Lecture15 SPT phases in 1D (I) (28.06.2021)
Lecture16 SPT phases in 1D (II) (01.07.2021)
Lecture17 Projected entangled pair state (05.07.2021)
Lecture18 PEPS algorithms (12.07.2021)
Lecture19 Tensor renormalization group (15.07.2021)
Lecture20 Tensor network renormalization (19.07.2021)

Exercises:

Exercise1 (tutorial: 22.04.2020, sample code in OPAL)
Exercise2 (tutorial: 06.05.2020)
Exercise3 (tutorial: 20.05.2020, sample code in OPAL)
Exercise4 (tutorial: 10.06.2020, sample code in OPAL)
Exercise5 (tutorial: 24.06.2020, sample code in OPAL)
Exercise6 (tutorial: 08.07.2020)
Exercise7 (tutorial: 22.07.2020, sample code in OPAL)

Reference:

• F. Verstraete, V. Murg, and J. I. Cirac, Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems, Adv. Phys. 57,143 (2008).

• U. Schollwöck, The density-matrix renormalization group in the age of matrix product states, Ann. Phys. 326, 96 (2011).

• R. Orús, A practical introduction to tensor networks: matrix product states and projected tntangled pair states, Ann. Phys. 349, 117 (2014).

• J. I. Cirac, D. Perez-Garcia, N. Schuch, and F. Verstraete, Matrix product states and projected entangled pair states: Concepts, symmetries, theorems, Rev. Mod. Phys. 93, 045003 (2021).

• J. von Delft, Lecture on Tensor Networks (SS2020); see link.