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@@ -10,7 +10,7 @@ This website collects information from the tensor4all group which is working on
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The <a href="https://tensor4all.discourse.group" style="color: #1976D2; text-decoration: none; font-weight: bold;">tensor4all discourse forum</a> is now open!
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Please feel free to ask questions and discuss your ideas with us.
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Please feel free to ask questions and discuss your ideas with us.
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A pedagogical introduction to tensor network methods, which includes an overview of the existing literature and also new algorithms, can be found in:
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> Yuriel Núñez Fernández, Marc K. Ritter, Matthieu Jeannin, Jheng-Wei Li, Thomas Kloss, Thibaud Louvet, Satoshi Terasaki, Olivier Parcollet, Jan von Delft, Hiroshi Shinaoka, and Xavier Waintal, "Learning tensor networks with tensor cross interpolation: new algorithms and libraries", [arXiv:2407.02454](https://arxiv.org/abs/2407.02454).
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> Yuriel Núñez Fernández, Marc K. Ritter, Matthieu Jeannin, Jheng-Wei Li, Thomas Kloss, Thibaud Louvet, Satoshi Terasaki, Olivier Parcollet, Jan von Delft, Hiroshi Shinaoka, Xavier Waintal, "Learning tensor networks with tensor cross interpolation: New algorithms and libraries", [SciPost Phys. 18, 104 (2025)](https://www.scipost.org/SciPostPhys.18.3.104) · published 20 March 2025, [arXiv:2407.02454](https://arxiv.org/abs/2407.02454).
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Please check the [reference](reference.html) page for more information on TCI and quantics tensor trains.
We apply the tensor cross interpolation (TCI) algorithm to solve equilibrium quantum impurity problems with high precision based on the weak-coupling expansion. The TCI algorithm enables efficient evaluation of higher-order terms in perturbative expansions by factorizing high-dimensional integrals into low-dimensional ones.
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**High-resolution nonequilibrium GW calculations based on quantics tensor trains*<br>
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**Memory-Efficient Nonequilibrium Green's Function Framework Built On Quantics Tensor Trains*<br>
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Maksymilian Środa, Ken Inayoshi, Hiroshi Shinaoka, Philipp Werner<br>
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[Phys. Rev. Lett. 135, 226501 (2025)](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.135.226501)<br>
This paper demonstrates nonequilibrium GW simulations with high momentum resolution using quantics tensor train (QTT) representation, enabling the study of thermalization dynamics and transient Floquet physics during multi-cycle electric field pulses.
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**Learning low-rank tensor train representations: new algorithms and libraries*<br>
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Yuriel Núñez Fernández, Marc K. Ritter, Matthieu Jeannin, Jheng-Wei Li, Thomas Kloss, Thibaud Louvet, Satoshi Terasaki, Olivier Parcollet, Jan von Delft, Hiroshi Shinaoka, and Xavier Waintal<br>
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**Learning tensor networks with tensor cross interpolation: New algorithms and libraries*<br>
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Yuriel Núñez Fernández, Marc K. Ritter, Matthieu Jeannin, Jheng-Wei Li, Thomas Kloss, Thibaud Louvet, Satoshi Terasaki, Olivier Parcollet, Jan von Delft, Hiroshi Shinaoka, Xavier Waintal<br>
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[SciPost Phys. 18, 104 (2025)](https://www.scipost.org/SciPostPhys.18.3.104) · published 20 March 2025<br>
This paper provides a pedagogical introduction to tensor network methods, which includes an overview of the existing literature and also new algorithms.
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