Entropic Order Parameters for Categorical Symmetries in 2D-CFT
In this work, we propose an information theoretic order parameter able to characterize the presence and breaking of categorical symmetries in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(<...
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MDPI AG
2024-12-01
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| author | Javier Molina-Vilaplana Pablo Saura-Bastida Germán Sierra |
| author_facet | Javier Molina-Vilaplana Pablo Saura-Bastida Germán Sierra |
| author_sort | Javier Molina-Vilaplana |
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| description | In this work, we propose an information theoretic order parameter able to characterize the presence and breaking of categorical symmetries in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>-d rational conformal field theories (RCFTs). Specifically, we compute the quantum relative entropy between the ground states of RCFTs representing the critical point of phase transitions between different symmetry-broken phases of theories with categorical symmetries, and their symmetrized versions. We find that, at leading order in the high temperature limit, this relative entropy only depends on the expectation values of the quantum dimensions of the topological operators implementing the categorical symmetry. This dependence suggests that our proposal can be used to characterize the different broken phases of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>-d theories with categorical symmetries. |
| format | Article |
| id | doaj-art-d25281efb9eb4881afcc43d189e1f2d9 |
| institution | Kabale University |
| issn | 1099-4300 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
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| series | Entropy |
| spelling | doaj-art-d25281efb9eb4881afcc43d189e1f2d92024-12-27T14:25:05ZengMDPI AGEntropy1099-43002024-12-012612106410.3390/e26121064Entropic Order Parameters for Categorical Symmetries in 2D-CFTJavier Molina-Vilaplana0Pablo Saura-Bastida1Germán Sierra2Departamento de Automática, Ingeniería Eléctrica y Tecnología Electrónica, Universidad Politécnica de Cartagena, 30202 Cartagena, SpainDepartamento de Automática, Ingeniería Eléctrica y Tecnología Electrónica, Universidad Politécnica de Cartagena, 30202 Cartagena, SpainInstituto de Física Teórica, CSIC-Universidad Autónoma de Madrid, 28049 Madrid, SpainIn this work, we propose an information theoretic order parameter able to characterize the presence and breaking of categorical symmetries in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>-d rational conformal field theories (RCFTs). Specifically, we compute the quantum relative entropy between the ground states of RCFTs representing the critical point of phase transitions between different symmetry-broken phases of theories with categorical symmetries, and their symmetrized versions. We find that, at leading order in the high temperature limit, this relative entropy only depends on the expectation values of the quantum dimensions of the topological operators implementing the categorical symmetry. This dependence suggests that our proposal can be used to characterize the different broken phases of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>-d theories with categorical symmetries.https://www.mdpi.com/1099-4300/26/12/1064relative entropycategorical symmetriesconformal field theorysymmetry breaking |
| spellingShingle | Javier Molina-Vilaplana Pablo Saura-Bastida Germán Sierra Entropic Order Parameters for Categorical Symmetries in 2D-CFT Entropy relative entropy categorical symmetries conformal field theory symmetry breaking |
| title | Entropic Order Parameters for Categorical Symmetries in 2D-CFT |
| title_full | Entropic Order Parameters for Categorical Symmetries in 2D-CFT |
| title_fullStr | Entropic Order Parameters for Categorical Symmetries in 2D-CFT |
| title_full_unstemmed | Entropic Order Parameters for Categorical Symmetries in 2D-CFT |
| title_short | Entropic Order Parameters for Categorical Symmetries in 2D-CFT |
| title_sort | entropic order parameters for categorical symmetries in 2d cft |
| topic | relative entropy categorical symmetries conformal field theory symmetry breaking |
| url | https://www.mdpi.com/1099-4300/26/12/1064 |
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