| アイテムタイプ |
default_学術雑誌論文 / Journal Article(1) |
| タイトル |
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タイトル |
All-mode renormalization for tensor network with stochastic noise |
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言語 |
en |
| 言語 |
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言語 |
eng |
| キーワード |
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言語 |
en |
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主題Scheme |
Other |
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主題 |
Lattice field theory |
| キーワード |
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言語 |
en |
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主題Scheme |
Other |
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主題 |
Renormalization group |
| キーワード |
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言語 |
en |
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主題Scheme |
Other |
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主題 |
Statistical field theory |
| キーワード |
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言語 |
en |
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主題Scheme |
Other |
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主題 |
Quantum field theory |
| キーワード |
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言語 |
en |
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主題Scheme |
Other |
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主題 |
Monte Carlo methods |
| 資源タイプ |
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資源タイプ識別子 |
http://purl.org/coar/resource_type/c_6501 |
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資源タイプ |
journal article |
| アクセス権 |
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アクセス権 |
metadata only access |
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アクセス権URI |
http://purl.org/coar/access_right/c_14cb |
| 著者 |
Arai Erika
大木 洋
武田 真滋
Tomii Masaaki
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| 抄録 |
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内容記述タイプ |
Abstract |
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内容記述 |
In usual (nonstochastic) tensor network calculations, the truncated singular value decomposition is often used for approximating a tensor, and it causes systematic errors. By introducing stochastic noise in the approximation, however, one can avoid such systematic errors at the expense of statistical errors, which can be straightforwardly controlled. Therefore in principle, exact results can be obtained even at finite bond dimension up to the statistical errors. A previous study of the unbiased method implemented in tensor renormalization group algorithm, however, showed that the statistical errors for physical quantity are not negligible, and furthermore the computational cost is linearly proportional to a system volume. In this paper, we introduce a new way of stochastic noise such that the statistical error is suppressed, and moreover, in order to reduce the computational cost we propose common noise method whose cost is proportional to the logarithm of volume. We find that the method provides better accuracy for the free energy compared with the truncated singular value decomposition when applying to tensor renormalization group for Ising model on square lattice. Although the common noise method introduces systematic error originated from a correlation of noises, we show that the error can be described by a simple functional form in terms of the number of noises, thus the error can be straightforwardly controlled in an actual analysis. We also apply the method to the graph independent local truncation algorithm and show that the accuracy is further improved. |
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言語 |
en |
| 書誌情報 |
en : Physical Review D
巻 107,
号 11,
発行日 2023-06-01
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| 出版者 |
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出版者 |
American Physical Society |
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言語 |
en |
| ISSN |
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収録物識別子タイプ |
EISSN |
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収録物識別子 |
2470-0029 |
| DOI |
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識別子タイプ |
DOI |
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関連識別子 |
10.1103/PhysRevD.107.114515 |
| 権利 |
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権利情報 |
© American Physical Society. |
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言語 |
en |
https://doi.org/10.1103/PhysRevD.107.114515
