Teaching material for the course PHYS-E0510, Advanced Computational Methods in Physics D: Quantum many body and tensor networks, at Aalto University (2026).
Each of the five sessions comes with a set of lecture slides, a short set of lecture notes, and a Jupyter notebook reproducing the calculations discussed in the lecture. The notebooks also have questions that require you to modify the examples in order to answer them.
The Jupyter notebooks require that you install the following two libraries
Check the link of each library to know how to install it
- Session 1: Many-body interactions and classical symmetry broken magnetism
- Session 2: Many-body quantum magnets
- Session 3: Many-body correlated fermionic systems
- Session 4: Tensor networks for many-body quantum magnets
- Session 5: Tensor networks for many-body correlated fermionic systems
- Machine learning for quantum states (slides only, no notebook or lecture notes)
- Session 1: Many-body interactions and classical symmetry broken magnetism
- Session 2: Many-body quantum magnets
- Session 3: Many-body correlated fermionic systems
- Session 4: Tensor networks for many-body quantum magnets
- Session 5: Tensor networks for many-body correlated fermionic systems
Short silent films with captions, four per session, where in one to two minutes we see one idea of the session, with every number on screen computed with the same codes as the notebooks
Each link opens the film in a player on one page, and the mp4 files are in exercise_shorts
- Film 1.1: The exponential wall
- Film 1.2: Superexchange: from electrons to spins
- Film 1.3: Mean-field theory: the self-consistent loop
- Film 1.4: Classical order and frustration
- Film 2.1: A classical and a quantum magnet
- Film 2.2: Exact diagonalization
- Film 2.3: A magnetic field as a probe
- Film 2.4: Gapped or gapless?
- Film 3.1: Charge order in the many-body spectrum
- Film 3.2: The chemical potential as a gate
- Film 3.3: Is the Hubbard chain magnetic?
- Film 3.4: Spin-charge separation
- Film 4.1: Matrix product states
- Film 4.2: Entanglement and the area law
- Film 4.3: Entanglement at a phase transition
- Film 4.4: Fractionalization: the spin-1 chain
- Film 5.1: Fermions as spins: the Jordan-Wigner string
- Film 5.2: A charge density wave at a hundred sites
- Film 5.3: When is mean-field theory valid? The correlation entropy
- Film 5.4: The density matrix renormalization group
Recordings of the video lectures, from the previous edition of the course