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Tensor networks for quantum many-body systems - lecture 2
Multi angle
Authors : Bañuls, Mari Carmen (Author of the conference)
CIRM (Publisher )
81T17 - Renormalization group methods
81Q35 - Quantum mechanics on special spaces: manifolds, fractals, graphs, etc.
CIRM (Publisher )
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Abstract :
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.
MSC Codes : 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.
81T17 - Renormalization group methods
81Q35 - Quantum mechanics on special spaces: manifolds, fractals, graphs, etc.
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 29/03/2022 Conference Date : 15/03/2022 Subseries : Research talks arXiv category : Quantum Physics Mathematical Area(s) : Mathematical Physics Format : MP4 (.mp4) - HD Video Time : 01:29:18 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2022-03-15_Banuls_Part2.mp4 
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Information on the Event
Event Title : Random Tensors / Tenseurs aléatoiresEvent Organizers : Dartois, Stéphane ; De las Cuevas, Gemma ; Lancien, Cécilia ; Lionni, Luca ; Nechita, Ion Dates : 14/03/2022 - 18/03/2022 Event Year : 2022 Event URL : https://conferences.cirm-math.fr/2541.html
Citation Data
DOI : 10.24350/CIRM.V.19896603Cite this video as: Bañuls, Mari Carmen (2022). Tensor networks for quantum many-body systems - lecture 2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19896603 URI : http://dx.doi.org/10.24350/CIRM.V.19896603 |
See Also
- [Multi angle] The tensor Harish-Chandra-Itzykson-Zuber integral / Author of the conference Gurău, Răzvan.
- [Multi angle] Tensor PCA / Author of the conference Ben Arous, Gérard.
- [Multi angle] Tensor networks for quantum many-body systems - lecture 1 / Author of the conference Bañuls, Mari Carmen.
- [Multi angle] Asymptotic tensor powers of Banach spaces / Author of the conference Aubrun, Guillaume.
Bibliography
- CIRAC, J. Ignacio et VERSTRAETE, Frank. Renormalization and tensor product states in spin chains and lattices. Journal of physics a: mathematical and theoretical, 2009, vol. 42, no 50, p. 504004. - https://arxiv.org/abs/0910.1130
- 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
- ORÚS, Román. A practical introduction to tensor networks: Matrix product states and projected entangled pair states. Annals of physics, 2014, vol. 349, p. 117-158. - https://arxiv.org/abs/1306.2164
- BRIDGEMAN, Jacob C. et CHUBB, Christopher T. Hand-waving and interpretive dance: an introductory course on tensor networks. Journal of physics A: Mathematical and theoretical, 2017, vol. 50, no 22, p. 223001. - https://arxiv.org/abs/1603.03039
- 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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