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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-12-01
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| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/26/12/1064 |
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| Summary: | 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. |
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| ISSN: | 1099-4300 |