Scaling dimensions from linearized tensor renormalization group transformations
We show a way to perform the canonical renormalization group (RG) prescription in tensor space: write down the tensor RG equation, linearize it around a fixed-point tensor, and diagonalize the resulting linearized RG equation to obtain scaling dimensions. The tensor RG methods have had great success...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2021-04-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.3.023048 |
| _version_ | 1797211064323014656 |
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| author | Xinliang Lyu RuQing G. Xu Naoki Kawashima |
| author_facet | Xinliang Lyu RuQing G. Xu Naoki Kawashima |
| author_sort | Xinliang Lyu |
| collection | DOAJ |
| description | We show a way to perform the canonical renormalization group (RG) prescription in tensor space: write down the tensor RG equation, linearize it around a fixed-point tensor, and diagonalize the resulting linearized RG equation to obtain scaling dimensions. The tensor RG methods have had great success in producing accurate free energy compared with the conventional real-space RG schemes. However, the above-mentioned canonical procedure has not been implemented for general tensor-network-based RG schemes. We extend the success of the tensor methods further to extraction of scaling dimensions through the canonical RG prescription, without explicitly using the conformal field theory. This approach is benchmarked in the context of the Ising models in one dimension and two dimensions. Based on a pure RG argument, the proposed method has potential applications to three-dimensional systems, where the existing bread-and-butter method is inapplicable. |
| first_indexed | 2024-04-24T10:20:33Z |
| format | Article |
| id | doaj.art-7c30cd113a5a4154853623493a93e513 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:20:33Z |
| publishDate | 2021-04-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-7c30cd113a5a4154853623493a93e5132024-04-12T17:09:15ZengAmerican Physical SocietyPhysical Review Research2643-15642021-04-013202304810.1103/PhysRevResearch.3.023048Scaling dimensions from linearized tensor renormalization group transformationsXinliang LyuRuQing G. XuNaoki KawashimaWe show a way to perform the canonical renormalization group (RG) prescription in tensor space: write down the tensor RG equation, linearize it around a fixed-point tensor, and diagonalize the resulting linearized RG equation to obtain scaling dimensions. The tensor RG methods have had great success in producing accurate free energy compared with the conventional real-space RG schemes. However, the above-mentioned canonical procedure has not been implemented for general tensor-network-based RG schemes. We extend the success of the tensor methods further to extraction of scaling dimensions through the canonical RG prescription, without explicitly using the conformal field theory. This approach is benchmarked in the context of the Ising models in one dimension and two dimensions. Based on a pure RG argument, the proposed method has potential applications to three-dimensional systems, where the existing bread-and-butter method is inapplicable.http://doi.org/10.1103/PhysRevResearch.3.023048 |
| spellingShingle | Xinliang Lyu RuQing G. Xu Naoki Kawashima Scaling dimensions from linearized tensor renormalization group transformations Physical Review Research |
| title | Scaling dimensions from linearized tensor renormalization group transformations |
| title_full | Scaling dimensions from linearized tensor renormalization group transformations |
| title_fullStr | Scaling dimensions from linearized tensor renormalization group transformations |
| title_full_unstemmed | Scaling dimensions from linearized tensor renormalization group transformations |
| title_short | Scaling dimensions from linearized tensor renormalization group transformations |
| title_sort | scaling dimensions from linearized tensor renormalization group transformations |
| url | http://doi.org/10.1103/PhysRevResearch.3.023048 |
| work_keys_str_mv | AT xinlianglyu scalingdimensionsfromlinearizedtensorrenormalizationgrouptransformations AT ruqinggxu scalingdimensionsfromlinearizedtensorrenormalizationgrouptransformations AT naokikawashima scalingdimensionsfromlinearizedtensorrenormalizationgrouptransformations |