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index.md

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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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</p>
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<p style="margin: 10px 0; color: #424242;">
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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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</p>
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<a href="https://tensor4all.discourse.group" style="display: inline-block; background-color: #2196F3; color: white; padding: 12px 24px; text-decoration: none; border-radius: 6px; font-weight: bold; margin-top: 10px; transition: background-color 0.3s;" onmouseover="this.style.backgroundColor='#1976D2'" onmouseout="this.style.backgroundColor='#2196F3'">
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Join the Discussion →
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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.
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reference.md

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* *Tensor cross interpolation approach for quantum impurity problems based on the weak-coupling expansion*<br>
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Shuta Matsuura, Hiroshi Shinaoka, Philipp Werner, Naoto Tsuji<br>
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[Phys. Rev. B 111, 155150 (2025)](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.111.155150)<br>
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[arXiv:2501.12643](https://arxiv.org/abs/2501.12643)<br>
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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>
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[arXiv:2412.14032](https://arxiv.org/abs/2412.14032)<br>
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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>
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[arXiv:2407.02454](https://arxiv.org/abs/2407.02454)<br>
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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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