Two-particle calculations with quantics tensor trains: Solving the parquet equations
We present an application of quantics tensor trains (QTTs) and tensor cross interpolation (TCI) to the solution of a full set of self-consistent equations for multivariate functions, the so-called parquet equations. We show that the steps needed to evaluate the equations (Bethe-Salpeter equations, p...
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-04-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.7.023087 |
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| author | Stefan Rohshap Marc K. Ritter Hiroshi Shinaoka Jan von Delft Markus Wallerberger Anna Kauch |
| author_facet | Stefan Rohshap Marc K. Ritter Hiroshi Shinaoka Jan von Delft Markus Wallerberger Anna Kauch |
| author_sort | Stefan Rohshap |
| collection | DOAJ |
| description | We present an application of quantics tensor trains (QTTs) and tensor cross interpolation (TCI) to the solution of a full set of self-consistent equations for multivariate functions, the so-called parquet equations. We show that the steps needed to evaluate the equations (Bethe-Salpeter equations, parquet equation, and Schwinger-Dyson equation) can be decomposed into basic operations on the QTT-TCI compressed objects. The repeated application of these operations does not lead to a loss of accuracy beyond a specified tolerance and the iterative scheme converges even for numerically demanding parameters. As examples, we take the Hubbard model in the atomic limit and the single impurity Anderson model, where the basic objects in parquet equations, the two-particle vertices, depend on three frequencies, but not on momenta. The results show that this approach is able to overcome major computational bottlenecks of standard numerical methods. The applied methods allow for an exponential increase of the number of grid points included in the calculations, and a corresponding exponential reduction of the computational error, for a linear increase in computational cost. |
| format | Article |
| id | doaj-art-fbbe9a7f01ce43b089c67f3f955fb923 |
| institution | OA Journals |
| issn | 2643-1564 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj-art-fbbe9a7f01ce43b089c67f3f955fb9232025-08-20T02:24:51ZengAmerican Physical SocietyPhysical Review Research2643-15642025-04-017202308710.1103/PhysRevResearch.7.023087Two-particle calculations with quantics tensor trains: Solving the parquet equationsStefan RohshapMarc K. RitterHiroshi ShinaokaJan von DelftMarkus WallerbergerAnna KauchWe present an application of quantics tensor trains (QTTs) and tensor cross interpolation (TCI) to the solution of a full set of self-consistent equations for multivariate functions, the so-called parquet equations. We show that the steps needed to evaluate the equations (Bethe-Salpeter equations, parquet equation, and Schwinger-Dyson equation) can be decomposed into basic operations on the QTT-TCI compressed objects. The repeated application of these operations does not lead to a loss of accuracy beyond a specified tolerance and the iterative scheme converges even for numerically demanding parameters. As examples, we take the Hubbard model in the atomic limit and the single impurity Anderson model, where the basic objects in parquet equations, the two-particle vertices, depend on three frequencies, but not on momenta. The results show that this approach is able to overcome major computational bottlenecks of standard numerical methods. The applied methods allow for an exponential increase of the number of grid points included in the calculations, and a corresponding exponential reduction of the computational error, for a linear increase in computational cost.http://doi.org/10.1103/PhysRevResearch.7.023087 |
| spellingShingle | Stefan Rohshap Marc K. Ritter Hiroshi Shinaoka Jan von Delft Markus Wallerberger Anna Kauch Two-particle calculations with quantics tensor trains: Solving the parquet equations Physical Review Research |
| title | Two-particle calculations with quantics tensor trains: Solving the parquet equations |
| title_full | Two-particle calculations with quantics tensor trains: Solving the parquet equations |
| title_fullStr | Two-particle calculations with quantics tensor trains: Solving the parquet equations |
| title_full_unstemmed | Two-particle calculations with quantics tensor trains: Solving the parquet equations |
| title_short | Two-particle calculations with quantics tensor trains: Solving the parquet equations |
| title_sort | two particle calculations with quantics tensor trains solving the parquet equations |
| url | http://doi.org/10.1103/PhysRevResearch.7.023087 |
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