Tensor-network renormalization approach to the q-state clock model
We simulate the phase diagram and critical behavior of the q-state clock model on the square lattice by using the state-of-the-art loop optimization for tensor-network renormalization (loop-TNR) algorithm. The two phase transition points for q≥5 are determined with very high accuracy. Furthermore, b...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2022-05-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.4.023159 |
| _version_ | 1797210755969318912 |
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| author | Guanrong Li Kwok Ho Pai Zheng-Cheng Gu |
| author_facet | Guanrong Li Kwok Ho Pai Zheng-Cheng Gu |
| author_sort | Guanrong Li |
| collection | DOAJ |
| description | We simulate the phase diagram and critical behavior of the q-state clock model on the square lattice by using the state-of-the-art loop optimization for tensor-network renormalization (loop-TNR) algorithm. The two phase transition points for q≥5 are determined with very high accuracy. Furthermore, by computing the conformal scaling dimensions for both transition points, we are able to determine the radius R of the compactified boson theories at both transition points with high precision. In particular, the radius R at higher temperature phase transition point is precisely the same as the one predicted by Berezinskii-Kosterlitz-Thouless (BKT) transition. Moreover, we find that the fixed-point tensors at higher temperature transition point also converge to the same one approximately for large enough q and the corresponding operator product expansion (OPE) coefficient of the compactified boson theory can also be read out directly from the fixed-point tensor. |
| first_indexed | 2024-04-24T10:15:39Z |
| format | Article |
| id | doaj.art-e2240f5383a54a22a46b75a64b1e5dbe |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:15:39Z |
| publishDate | 2022-05-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-e2240f5383a54a22a46b75a64b1e5dbe2024-04-12T17:21:22ZengAmerican Physical SocietyPhysical Review Research2643-15642022-05-014202315910.1103/PhysRevResearch.4.023159Tensor-network renormalization approach to the q-state clock modelGuanrong LiKwok Ho PaiZheng-Cheng GuWe simulate the phase diagram and critical behavior of the q-state clock model on the square lattice by using the state-of-the-art loop optimization for tensor-network renormalization (loop-TNR) algorithm. The two phase transition points for q≥5 are determined with very high accuracy. Furthermore, by computing the conformal scaling dimensions for both transition points, we are able to determine the radius R of the compactified boson theories at both transition points with high precision. In particular, the radius R at higher temperature phase transition point is precisely the same as the one predicted by Berezinskii-Kosterlitz-Thouless (BKT) transition. Moreover, we find that the fixed-point tensors at higher temperature transition point also converge to the same one approximately for large enough q and the corresponding operator product expansion (OPE) coefficient of the compactified boson theory can also be read out directly from the fixed-point tensor.http://doi.org/10.1103/PhysRevResearch.4.023159 |
| spellingShingle | Guanrong Li Kwok Ho Pai Zheng-Cheng Gu Tensor-network renormalization approach to the q-state clock model Physical Review Research |
| title | Tensor-network renormalization approach to the q-state clock model |
| title_full | Tensor-network renormalization approach to the q-state clock model |
| title_fullStr | Tensor-network renormalization approach to the q-state clock model |
| title_full_unstemmed | Tensor-network renormalization approach to the q-state clock model |
| title_short | Tensor-network renormalization approach to the q-state clock model |
| title_sort | tensor network renormalization approach to the q state clock model |
| url | http://doi.org/10.1103/PhysRevResearch.4.023159 |
| work_keys_str_mv | AT guanrongli tensornetworkrenormalizationapproachtotheqstateclockmodel AT kwokhopai tensornetworkrenormalizationapproachtotheqstateclockmodel AT zhengchenggu tensornetworkrenormalizationapproachtotheqstateclockmodel |