Modular flow of excited states
Abstract We develop new techniques for studying the modular and the relative modular flows of general excited states. We show that the class of states obtained by acting on the vacuum (or any cyclic and separating state) with invertible operators from the algebr...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Springer Berlin Heidelberg
2021
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| Online Access: | https://hdl.handle.net/1721.1/136738 |
| _version_ | 1826200100501716992 |
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| author | Lashkari, Nima Liu, Hong Rajagopal, Srivatsan |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Lashkari, Nima Liu, Hong Rajagopal, Srivatsan |
| author_sort | Lashkari, Nima |
| collection | MIT |
| description | Abstract
We develop new techniques for studying the modular and the relative modular flows of general excited states. We show that the class of states obtained by acting on the vacuum (or any cyclic and separating state) with invertible operators from the algebra of a region is dense in the Hilbert space. This enables us to express the modular and the relative modular operators, as well as the relative entropies of generic excited states in terms of the vacuum modular operator and the operator that creates the state. In particular, the modular and the relative modular flows of any state can be expanded in terms of the modular flow of operators in vacuum. We illustrate the formalism with simple examples including states close to the vacuum, and coherent and squeezed states in generalized free field theory. |
| first_indexed | 2024-09-23T11:31:32Z |
| format | Article |
| id | mit-1721.1/136738 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:31:32Z |
| publishDate | 2021 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1367382024-01-02T20:40:23Z Modular flow of excited states Lashkari, Nima Liu, Hong Rajagopal, Srivatsan Massachusetts Institute of Technology. Center for Theoretical Physics Abstract We develop new techniques for studying the modular and the relative modular flows of general excited states. We show that the class of states obtained by acting on the vacuum (or any cyclic and separating state) with invertible operators from the algebra of a region is dense in the Hilbert space. This enables us to express the modular and the relative modular operators, as well as the relative entropies of generic excited states in terms of the vacuum modular operator and the operator that creates the state. In particular, the modular and the relative modular flows of any state can be expanded in terms of the modular flow of operators in vacuum. We illustrate the formalism with simple examples including states close to the vacuum, and coherent and squeezed states in generalized free field theory. 2021-10-29T17:16:02Z 2021-10-29T17:16:02Z 2021-09-24 2021-09-26T03:11:52Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/136738 Journal of High Energy Physics. 2021 Sep 24;2021(9):166 PUBLISHER_CC en https://doi.org/10.1007/JHEP09(2021)166 Creative Commons Attribution https://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Lashkari, Nima Liu, Hong Rajagopal, Srivatsan Modular flow of excited states |
| title | Modular flow of excited states |
| title_full | Modular flow of excited states |
| title_fullStr | Modular flow of excited states |
| title_full_unstemmed | Modular flow of excited states |
| title_short | Modular flow of excited states |
| title_sort | modular flow of excited states |
| url | https://hdl.handle.net/1721.1/136738 |
| work_keys_str_mv | AT lashkarinima modularflowofexcitedstates AT liuhong modularflowofexcitedstates AT rajagopalsrivatsan modularflowofexcitedstates |