Gluing together modular flows with free fermions
Abstract We revisit the calculation of multi-interval modular Hamiltonians for free fermions using a Euclidean path integral approach. We show how the multi-interval modular flow is obtained by gluing together the single interval modular flows. Using this relation, we obtain an exact expression for...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-04-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP04(2019)045 |
| _version_ | 1818126616539168768 |
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| author | Gabriel Wong |
| author_facet | Gabriel Wong |
| author_sort | Gabriel Wong |
| collection | DOAJ |
| description | Abstract We revisit the calculation of multi-interval modular Hamiltonians for free fermions using a Euclidean path integral approach. We show how the multi-interval modular flow is obtained by gluing together the single interval modular flows. Using this relation, we obtain an exact expression for the multi-interval modular Hamiltonian and entanglement entropy in agreement with existing results. An essential ingredient in our derivation is the introduction of the modular action. This determines the non-local field theory describing the free fermion reduced density matrix, and makes manifest it’s non-local conformal symmetry and U(1) Kacs-Moody symmetry. |
| first_indexed | 2024-12-11T07:04:18Z |
| format | Article |
| id | doaj.art-4b4596096d3b4d848034c1ae0c9fd6d2 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-11T07:04:18Z |
| publishDate | 2019-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-4b4596096d3b4d848034c1ae0c9fd6d22022-12-22T01:16:32ZengSpringerOpenJournal of High Energy Physics1029-84792019-04-012019412810.1007/JHEP04(2019)045Gluing together modular flows with free fermionsGabriel Wong0Department of Physics, Fudan UniversityAbstract We revisit the calculation of multi-interval modular Hamiltonians for free fermions using a Euclidean path integral approach. We show how the multi-interval modular flow is obtained by gluing together the single interval modular flows. Using this relation, we obtain an exact expression for the multi-interval modular Hamiltonian and entanglement entropy in agreement with existing results. An essential ingredient in our derivation is the introduction of the modular action. This determines the non-local field theory describing the free fermion reduced density matrix, and makes manifest it’s non-local conformal symmetry and U(1) Kacs-Moody symmetry.http://link.springer.com/article/10.1007/JHEP04(2019)045Boundary Quantum Field TheoryConformal and W SymmetryConformal Field Theory |
| spellingShingle | Gabriel Wong Gluing together modular flows with free fermions Journal of High Energy Physics Boundary Quantum Field Theory Conformal and W Symmetry Conformal Field Theory |
| title | Gluing together modular flows with free fermions |
| title_full | Gluing together modular flows with free fermions |
| title_fullStr | Gluing together modular flows with free fermions |
| title_full_unstemmed | Gluing together modular flows with free fermions |
| title_short | Gluing together modular flows with free fermions |
| title_sort | gluing together modular flows with free fermions |
| topic | Boundary Quantum Field Theory Conformal and W Symmetry Conformal Field Theory |
| url | http://link.springer.com/article/10.1007/JHEP04(2019)045 |
| work_keys_str_mv | AT gabrielwong gluingtogethermodularflowswithfreefermions |