Tensor networks for quantum many-body systems - lecture 2 | Vidéo | Carmin.tv

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Tensor networks for quantum many-body systems - lecture 2

By Mari Carmen Banuls

Appears in collection : Random Tensors / Tenseurs aléatoires

The term Tensor Network States (TNS) has become a common one in the context of numerical studies of quantum many-body problems. It refers to a number of families that represent different ansatzes for the efficient description of the state of a quantum many-body system. The first of these families, Matrix Product States (MPS), lies at the basis of Density Matrix Renormalization Group methods, which have become the most precise tool for the study of one dimensional quantum many-body systems. Their natural generalization to two or higher dimensions, the Projected Entanglement Pair States (PEPS) are good candidates to describe the physics of higher dimensional lattices. They can be used to study equilibrium properties, as ground and thermal states, but also dynamics. Quantum information gives us some tools to understand why these families are expected to be good ansatzes for the physically relevant states, and some of the limitations connected to the simulation algorithms. Originally introduced in the context of condensed matter physics, these methods have become a state-of-the-art technique for strongly correlated one-dimensional systems. Their applicability extends nevertheless to other fields. These lectures will present the fundamental concepts behind TNS methods, the main families and the basic algorithms available.

Information about the video

Date of recording 15/03/2022
Date of publication 29/03/2022
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19896603
Cite this video Banuls, Mari Carmen (15/03/2022). Tensor networks for quantum many-body systems - lecture 2. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19896603
URL https://dx.doi.org/10.24350/CIRM.V.19896603

Domain(s)

Quantum Physics

Bibliography

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SCHOLLWÖCK, Ulrich. The density-matrix renormalization group in the age of matrix product states. Annals of physics, 2011, vol. 326, no 1, p. 96-192. - https://arxiv.org/abs/1008.3477
VERSTRAETE, F., CIRAC, J. I., et MURG, V. Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems. arXiv preprint 0907.2796. URL http://arxiv. org/abs/0907.2796, 2009. - https://arxiv.org/abs/0907.2796
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SILVI, Pietro, TSCHIRSICH, Ferdinand, GERSTER, Matthias, et al. The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems. SciPost Physics Lecture Notes, 2019, p. 008. - https://arxiv.org/abs/1710.03733
MONTANGERO, Simone, MONTANGERO, et EVENSON. Introduction to Tensor Network Methods. Springer International Publishing, 2018. - https://doi.org/10.1007/978-3-030-01409-4

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