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TensorTutorials

Jacob Bridgeman, Lander Burgelman, Lukas Devos, Jutho Haegeman, Daan Maertens, Bram Vancraeynest-De Cuiper and Kevin Vervoort

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Creative Commons License – This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International.

Contents

Preliminaries

1. Getting Started with Numerics
2. Useful Resources

Introduction to Quantum Many-Body Physics

3. Quantum Mechanics and its Postulates
4. The Hilbert Space of Many-Body Physics
5. Fock Space and Second Quantisation
6. Interesting States and Observables in Quantum Many-Body Physics
7. Quantum-to-Classical Mapping

Tensors and Tensor Networks

8. (Multi-) Linear Algebra
9. Tensor Network Theory
10. Tensor Network States
11. Symmetries in Quantum Many-Body Physics

Matrix Product States

12. Matrix Product States
13. Infinite Matrix Product States
14. A Simple Tensor Network Algorithm
15. Matrix Product Operators and Applications

Tensor Network Algorithms

16. Fixed-Point algorithms
17. Time Evolution

In-Depth Tutorials

18. A Symmetric Tensor Deep Dive: Constructing Your First Tensor Map
19. Finite Entanglement Scaling

Other

20. References

QuantumGroup@UGent

Lecture (PDF)
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