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Résumé |
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.
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