Organisation des séminaires et calendrier

Abstract: 

These lectures will provide an introduction to tensor-network methods in quantum many-body physics, with an emphasis on matrix-product states (MPS).

• Basic tensor-network language, including graphical notation, virtual indices, bond dimensions, gauge freedom, canonical forms, QR and singular-value decompositions, and the role of entanglement in controlling the efficiency of the representation.
• Main MPS algorithms, including contractions, correlation functions, matrix-product operators, DMRG, and time-evolution methods.
• Brief introduction to projected entangled-pair states (PEPS) as a higher-dimensional generalization of MPS, together with the basic ideas behind approximate PEPS contraction.
• Tensor-network representations of mixed states, quantum channels, and Lindblad dynamics, with applications to thermal states and open quantum systems.

Based on https://arxiv.org/abs/2606.24803.

Website: courses.ipht.fr
Livestream: youtube.com/IPhT-TV (free access)
Videoconference (non-IPhT attendees): to receive the links join the course newsletter, see courses.ipht.fr/subscriptions

Abstract: 

These lectures will provide an introduction to tensor-network methods in quantum many-body physics, with an emphasis on matrix-product states (MPS).

• Basic tensor-network language, including graphical notation, virtual indices, bond dimensions, gauge freedom, canonical forms, QR and singular-value decompositions, and the role of entanglement in controlling the efficiency of the representation.
• Main MPS algorithms, including contractions, correlation functions, matrix-product operators, DMRG, and time-evolution methods.
• Brief introduction to projected entangled-pair states (PEPS) as a higher-dimensional generalization of MPS, together with the basic ideas behind approximate PEPS contraction.
• Tensor-network representations of mixed states, quantum channels, and Lindblad dynamics, with applications to thermal states and open quantum systems.

Based on https://arxiv.org/abs/2606.24803.

Website: courses.ipht.fr
Livestream: youtube.com/IPhT-TV (free access)
Videoconference (non-IPhT attendees): to receive the links join the course newsletter, see courses.ipht.fr/subscriptions

I will discuss conformal field theory on a vast class of d-dimensional manifolds, built by gluing cylinders and spheres. These manifolds carry a notion of genus, with genus zero corresponding to the sphere, and genus one to finite temperature CFT. 

I will explain how conformal blocks on these manifolds are related to quantum Hitchin integrable systems, and to the Wess-Zumino-Novikov-Witten models of 2d CFT. In particular, I will use the integrable Hamiltonians for deriving differential equations for d-dimensional conformal blocks. 

These ideas generalize the relation between sphere conformal blocks and Gaudin integrable models, and embed d-dimensional conformal blocks in 2d CFTs and supersymmetric gauge theories.

Based on joint work with Ilija Burić, Francesco Russo and Volker Schomerus (to appear)

Abstract: 

These lectures will provide an introduction to tensor-network methods in quantum many-body physics, with an emphasis on matrix-product states (MPS).

• Basic tensor-network language, including graphical notation, virtual indices, bond dimensions, gauge freedom, canonical forms, QR and singular-value decompositions, and the role of entanglement in controlling the efficiency of the representation.
• Main MPS algorithms, including contractions, correlation functions, matrix-product operators, DMRG, and time-evolution methods.
• Brief introduction to projected entangled-pair states (PEPS) as a higher-dimensional generalization of MPS, together with the basic ideas behind approximate PEPS contraction.
• Tensor-network representations of mixed states, quantum channels, and Lindblad dynamics, with applications to thermal states and open quantum systems.

Based on https://arxiv.org/abs/2606.24803.

Website: courses.ipht.fr
Livestream: youtube.com/IPhT-TV (free access)
Videoconference (non-IPhT attendees): to receive the links join the course newsletter, see courses.ipht.fr/subscriptions