Constructible reality condition of pseudo entropy via pseudo-Hermiticity
Abstract As a generalization of entanglement entropy, pseudo entropy is not always real. The real-valued pseudo entropy has promising applications in holography and quantum phase transition. We apply the notion of pseudo-Hermiticity to formulate the reality condition of pseudo entropy. We find the g...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2023-05-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP05(2023)021 |
| _version_ | 1797736485477154816 |
|---|---|
| author | Wu-zhong Guo Song He Yu-Xuan Zhang |
| author_facet | Wu-zhong Guo Song He Yu-Xuan Zhang |
| author_sort | Wu-zhong Guo |
| collection | DOAJ |
| description | Abstract As a generalization of entanglement entropy, pseudo entropy is not always real. The real-valued pseudo entropy has promising applications in holography and quantum phase transition. We apply the notion of pseudo-Hermiticity to formulate the reality condition of pseudo entropy. We find the general form of the transition matrix for which the eigenvalues of the reduced transition matrix possess real or complex pairs of eigenvalues. Further, we find a class of transition matrices for which the pseudo (Rényi) entropies are non-negative. Some known examples which give real pseudo entropy in quantum field theories can be explained in our framework. Our results offer a novel method to generate the transition matrix with real pseudo entropy. Finally, we show the reality condition for pseudo entropy is related to the Tomita-Takesaki modular theory for quantum field theory. |
| first_indexed | 2024-03-12T13:14:34Z |
| format | Article |
| id | doaj.art-7286674b892e493a8421bf9f50b486ff |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-12T13:14:34Z |
| publishDate | 2023-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-7286674b892e493a8421bf9f50b486ff2023-08-27T11:04:55ZengSpringerOpenJournal of High Energy Physics1029-84792023-05-012023513110.1007/JHEP05(2023)021Constructible reality condition of pseudo entropy via pseudo-HermiticityWu-zhong Guo0Song He1Yu-Xuan Zhang2School of Physics, Huazhong University of Science and TechnologyCenter for Theoretical Physics and College of Physics, Jilin UniversityCenter for Theoretical Physics and College of Physics, Jilin UniversityAbstract As a generalization of entanglement entropy, pseudo entropy is not always real. The real-valued pseudo entropy has promising applications in holography and quantum phase transition. We apply the notion of pseudo-Hermiticity to formulate the reality condition of pseudo entropy. We find the general form of the transition matrix for which the eigenvalues of the reduced transition matrix possess real or complex pairs of eigenvalues. Further, we find a class of transition matrices for which the pseudo (Rényi) entropies are non-negative. Some known examples which give real pseudo entropy in quantum field theories can be explained in our framework. Our results offer a novel method to generate the transition matrix with real pseudo entropy. Finally, we show the reality condition for pseudo entropy is related to the Tomita-Takesaki modular theory for quantum field theory.https://doi.org/10.1007/JHEP05(2023)021AdS-CFT CorrespondenceConformal and W SymmetryField Theories in Lower DimensionsHolography and Condensed Matter Physics (AdS/CMT) |
| spellingShingle | Wu-zhong Guo Song He Yu-Xuan Zhang Constructible reality condition of pseudo entropy via pseudo-Hermiticity Journal of High Energy Physics AdS-CFT Correspondence Conformal and W Symmetry Field Theories in Lower Dimensions Holography and Condensed Matter Physics (AdS/CMT) |
| title | Constructible reality condition of pseudo entropy via pseudo-Hermiticity |
| title_full | Constructible reality condition of pseudo entropy via pseudo-Hermiticity |
| title_fullStr | Constructible reality condition of pseudo entropy via pseudo-Hermiticity |
| title_full_unstemmed | Constructible reality condition of pseudo entropy via pseudo-Hermiticity |
| title_short | Constructible reality condition of pseudo entropy via pseudo-Hermiticity |
| title_sort | constructible reality condition of pseudo entropy via pseudo hermiticity |
| topic | AdS-CFT Correspondence Conformal and W Symmetry Field Theories in Lower Dimensions Holography and Condensed Matter Physics (AdS/CMT) |
| url | https://doi.org/10.1007/JHEP05(2023)021 |
| work_keys_str_mv | AT wuzhongguo constructiblerealityconditionofpseudoentropyviapseudohermiticity AT songhe constructiblerealityconditionofpseudoentropyviapseudohermiticity AT yuxuanzhang constructiblerealityconditionofpseudoentropyviapseudohermiticity |