Target space entanglement entropy
Abstract We define a notion of target space entanglement entropy. Rather than partitioning the base space on which the theory is defined, we consider partitions of the target space. This is the physical case of interest for first-quantized theories, such as worldsheet string theory. We associate to...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2023-03-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP03(2023)111 |
| _version_ | 1797795942134448128 |
|---|---|
| author | Edward A. Mazenc Daniel Ranard |
| author_facet | Edward A. Mazenc Daniel Ranard |
| author_sort | Edward A. Mazenc |
| collection | DOAJ |
| description | Abstract We define a notion of target space entanglement entropy. Rather than partitioning the base space on which the theory is defined, we consider partitions of the target space. This is the physical case of interest for first-quantized theories, such as worldsheet string theory. We associate to each subregion of the target space a suitably chosen subalgebra of observables A $$ \mathcal{A} $$ . The entanglement entropy is calculated as the entropy of the density matrix restricted to A $$ \mathcal{A} $$ . As an example, we illustrate our framework by computing spatial entanglement in first-quantized many-body quantum mechanics. The algebra A $$ \mathcal{A} $$ is chosen to reproduce the entanglement entropy obtained by embedding the state in the fixed particle sub-sector of the second-quantized Hilbert space. We then generalize our construction to the quantum field-theoretical setting. |
| first_indexed | 2024-03-13T03:25:38Z |
| format | Article |
| id | doaj.art-d7506baa0b814342aa93ad552c639ac9 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-13T03:25:38Z |
| publishDate | 2023-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-d7506baa0b814342aa93ad552c639ac92023-06-25T11:04:41ZengSpringerOpenJournal of High Energy Physics1029-84792023-03-012023313310.1007/JHEP03(2023)111Target space entanglement entropyEdward A. Mazenc0Daniel Ranard1Stanford Institute for Theoretical Physics, Stanford UniversityStanford Institute for Theoretical Physics, Stanford UniversityAbstract We define a notion of target space entanglement entropy. Rather than partitioning the base space on which the theory is defined, we consider partitions of the target space. This is the physical case of interest for first-quantized theories, such as worldsheet string theory. We associate to each subregion of the target space a suitably chosen subalgebra of observables A $$ \mathcal{A} $$ . The entanglement entropy is calculated as the entropy of the density matrix restricted to A $$ \mathcal{A} $$ . As an example, we illustrate our framework by computing spatial entanglement in first-quantized many-body quantum mechanics. The algebra A $$ \mathcal{A} $$ is chosen to reproduce the entanglement entropy obtained by embedding the state in the fixed particle sub-sector of the second-quantized Hilbert space. We then generalize our construction to the quantum field-theoretical setting.https://doi.org/10.1007/JHEP03(2023)111AdS-CFT CorrespondenceM(atrix) TheoriesSigma Models |
| spellingShingle | Edward A. Mazenc Daniel Ranard Target space entanglement entropy Journal of High Energy Physics AdS-CFT Correspondence M(atrix) Theories Sigma Models |
| title | Target space entanglement entropy |
| title_full | Target space entanglement entropy |
| title_fullStr | Target space entanglement entropy |
| title_full_unstemmed | Target space entanglement entropy |
| title_short | Target space entanglement entropy |
| title_sort | target space entanglement entropy |
| topic | AdS-CFT Correspondence M(atrix) Theories Sigma Models |
| url | https://doi.org/10.1007/JHEP03(2023)111 |
| work_keys_str_mv | AT edwardamazenc targetspaceentanglemententropy AT danielranard targetspaceentanglemententropy |