A Practical Guide to the Numerical Implementation of Tensor Networks I: Contractions, Decompositions, and Gauge Freedom
We present an overview of the key ideas and skills necessary to begin implementing tensor network methods numerically, which is intended to facilitate the practical application of tensor network methods for researchers that are already versed with their theoretical foundations. These skills include...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2022-06-01
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| Series: | Frontiers in Applied Mathematics and Statistics |
| Subjects: | |
| Online Access: | https://www.frontiersin.org/articles/10.3389/fams.2022.806549/full |
| _version_ | 1818164300919865344 |
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| author | Glen Evenbly |
| author_facet | Glen Evenbly |
| author_sort | Glen Evenbly |
| collection | DOAJ |
| description | We present an overview of the key ideas and skills necessary to begin implementing tensor network methods numerically, which is intended to facilitate the practical application of tensor network methods for researchers that are already versed with their theoretical foundations. These skills include an introduction to the contraction of tensor networks, to optimal tensor decompositions, and to the manipulation of gauge degrees of freedom in tensor networks. The topics presented are of key importance to many common tensor network algorithms such as DMRG, TEBD, TRG, PEPS, and MERA. |
| first_indexed | 2024-12-11T17:03:16Z |
| format | Article |
| id | doaj.art-75e83490ad2d48b79bf56003b3a29609 |
| institution | Directory Open Access Journal |
| issn | 2297-4687 |
| language | English |
| last_indexed | 2024-12-11T17:03:16Z |
| publishDate | 2022-06-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Applied Mathematics and Statistics |
| spelling | doaj.art-75e83490ad2d48b79bf56003b3a296092022-12-22T00:57:47ZengFrontiers Media S.A.Frontiers in Applied Mathematics and Statistics2297-46872022-06-01810.3389/fams.2022.806549806549A Practical Guide to the Numerical Implementation of Tensor Networks I: Contractions, Decompositions, and Gauge FreedomGlen EvenblyWe present an overview of the key ideas and skills necessary to begin implementing tensor network methods numerically, which is intended to facilitate the practical application of tensor network methods for researchers that are already versed with their theoretical foundations. These skills include an introduction to the contraction of tensor networks, to optimal tensor decompositions, and to the manipulation of gauge degrees of freedom in tensor networks. The topics presented are of key importance to many common tensor network algorithms such as DMRG, TEBD, TRG, PEPS, and MERA.https://www.frontiersin.org/articles/10.3389/fams.2022.806549/fulltensor network algorithmMPStensor contractionDMRGquantum many body theory |
| spellingShingle | Glen Evenbly A Practical Guide to the Numerical Implementation of Tensor Networks I: Contractions, Decompositions, and Gauge Freedom Frontiers in Applied Mathematics and Statistics tensor network algorithm MPS tensor contraction DMRG quantum many body theory |
| title | A Practical Guide to the Numerical Implementation of Tensor Networks I: Contractions, Decompositions, and Gauge Freedom |
| title_full | A Practical Guide to the Numerical Implementation of Tensor Networks I: Contractions, Decompositions, and Gauge Freedom |
| title_fullStr | A Practical Guide to the Numerical Implementation of Tensor Networks I: Contractions, Decompositions, and Gauge Freedom |
| title_full_unstemmed | A Practical Guide to the Numerical Implementation of Tensor Networks I: Contractions, Decompositions, and Gauge Freedom |
| title_short | A Practical Guide to the Numerical Implementation of Tensor Networks I: Contractions, Decompositions, and Gauge Freedom |
| title_sort | practical guide to the numerical implementation of tensor networks i contractions decompositions and gauge freedom |
| topic | tensor network algorithm MPS tensor contraction DMRG quantum many body theory |
| url | https://www.frontiersin.org/articles/10.3389/fams.2022.806549/full |
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