Tensor network finite-size scaling for two-dimensional 3-state clock model
We benchmark recently proposed tensor network based finite-size scaling analysis in ( Phys. Rev. B 2023 107 205123) against two-dimensional classical 3-state clock model. Due to the higher complexity of the model, more complicated crossover behavior is observed. We advocate that the crossover behavi...
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| Format: | Article |
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IOP Publishing
2025-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/add048 |
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| author | Debasmita Maiti Sing-Hong Chan Pochung Chen |
| author_facet | Debasmita Maiti Sing-Hong Chan Pochung Chen |
| author_sort | Debasmita Maiti |
| collection | DOAJ |
| description | We benchmark recently proposed tensor network based finite-size scaling analysis in ( Phys. Rev. B 2023 107 205123) against two-dimensional classical 3-state clock model. Due to the higher complexity of the model, more complicated crossover behavior is observed. We advocate that the crossover behavior can be understood from the perspective of finite bond dimension inducing relevant perturbation. This leads to a general strategy to best estimate the critical properties for a given set of control parameters. For the critical temperature $T_\textrm{c}$ , the relative error at the order of 10 ^−7 can be reached with bond dimension D = 70. On the other hand, with bond dimension D = 60, the relative errors of the critical exponents $\nu, \beta, \alpha$ are at the order of 10 ^−2 . Increasing the bond dimension to D = 90, these relative errors can be reduced at least to the order of 10 ^−3 . In all cases our results indicate that the errors can be systematically reduced by increasing the bond dimension and the stacking number. |
| format | Article |
| id | doaj-art-959b59ac695d4fb8bbe4c303b91aeee8 |
| institution | Kabale University |
| issn | 1367-2630 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj-art-959b59ac695d4fb8bbe4c303b91aeee82025-08-20T03:48:30ZengIOP PublishingNew Journal of Physics1367-26302025-01-0127505460110.1088/1367-2630/add048Tensor network finite-size scaling for two-dimensional 3-state clock modelDebasmita Maiti0Sing-Hong Chan1Pochung Chen2https://orcid.org/0000-0002-8092-7177Department of Physics, National Tsing Hua University , Hsinchu 30013, TaiwanDepartment of Physics, National Tsing Hua University , Hsinchu 30013, TaiwanDepartment of Physics, National Tsing Hua University , Hsinchu 30013, Taiwan; Physics Division, National Center for Theoretical Sciences , Taipei 10617, Taiwan; Frontier Center for Theory and Computation, National Tsing Hua University , Hsinchu 30013, TaiwanWe benchmark recently proposed tensor network based finite-size scaling analysis in ( Phys. Rev. B 2023 107 205123) against two-dimensional classical 3-state clock model. Due to the higher complexity of the model, more complicated crossover behavior is observed. We advocate that the crossover behavior can be understood from the perspective of finite bond dimension inducing relevant perturbation. This leads to a general strategy to best estimate the critical properties for a given set of control parameters. For the critical temperature $T_\textrm{c}$ , the relative error at the order of 10 ^−7 can be reached with bond dimension D = 70. On the other hand, with bond dimension D = 60, the relative errors of the critical exponents $\nu, \beta, \alpha$ are at the order of 10 ^−2 . Increasing the bond dimension to D = 90, these relative errors can be reduced at least to the order of 10 ^−3 . In all cases our results indicate that the errors can be systematically reduced by increasing the bond dimension and the stacking number.https://doi.org/10.1088/1367-2630/add048finite-size scalingtensor network renormalization3-state clock model |
| spellingShingle | Debasmita Maiti Sing-Hong Chan Pochung Chen Tensor network finite-size scaling for two-dimensional 3-state clock model New Journal of Physics finite-size scaling tensor network renormalization 3-state clock model |
| title | Tensor network finite-size scaling for two-dimensional 3-state clock model |
| title_full | Tensor network finite-size scaling for two-dimensional 3-state clock model |
| title_fullStr | Tensor network finite-size scaling for two-dimensional 3-state clock model |
| title_full_unstemmed | Tensor network finite-size scaling for two-dimensional 3-state clock model |
| title_short | Tensor network finite-size scaling for two-dimensional 3-state clock model |
| title_sort | tensor network finite size scaling for two dimensional 3 state clock model |
| topic | finite-size scaling tensor network renormalization 3-state clock model |
| url | https://doi.org/10.1088/1367-2630/add048 |
| work_keys_str_mv | AT debasmitamaiti tensornetworkfinitesizescalingfortwodimensional3stateclockmodel AT singhongchan tensornetworkfinitesizescalingfortwodimensional3stateclockmodel AT pochungchen tensornetworkfinitesizescalingfortwodimensional3stateclockmodel |