Mutual information for fermionic systems
We study the behavior of the mutual information (MI) in various quadratic fermionic chains, with and without pairing terms and both with short- and long-range hoppings. The models considered include the short-range limit and long-range versions of the Kitaev model as well, and also cases in which th...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2022-09-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.4.033212 |
| _version_ | 1797210621950820352 |
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| author | Luca Lepori Simone Paganelli Fabio Franchini Andrea Trombettoni |
| author_facet | Luca Lepori Simone Paganelli Fabio Franchini Andrea Trombettoni |
| author_sort | Luca Lepori |
| collection | DOAJ |
| description | We study the behavior of the mutual information (MI) in various quadratic fermionic chains, with and without pairing terms and both with short- and long-range hoppings. The models considered include the short-range limit and long-range versions of the Kitaev model as well, and also cases in which the area law for the entanglement entropy is—logarithmically or nonlogarithmically—violated. In all cases surveyed, when the area law is violated at most logarithmically, the MI is a monotonically increasing function of the conformal four-point ratio x. Where nonlogarithmic violations of the area law are present, nonmonotonic features can be observed in the MI, and the four-point ratio, as well as other natural combinations of the parameters, is found not to be sufficient to capture the whole structure of the MI with a collapse onto a single curve. We interpret this behavior as a sign that the structure of peaks is related to a nonuniversal spatial configuration of Bell pairs. For the model exhibiting a perfect volume law, the MI vanishes identically. For the Kitaev model the MI is vanishing for x→0 and it remains zero up to a finite x in the gapped case. In general, a larger range of the pairing corresponds to a reduction of the MI at small x. A discussion of the comparison with the results obtained by the anti–de Sitter/conformal field theory correspondence in the strong-coupling limit is presented. |
| first_indexed | 2024-04-24T10:13:31Z |
| format | Article |
| id | doaj.art-0ab8fadb00744638b62c812cde4eb424 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:13:31Z |
| publishDate | 2022-09-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-0ab8fadb00744638b62c812cde4eb4242024-04-12T17:24:32ZengAmerican Physical SocietyPhysical Review Research2643-15642022-09-014303321210.1103/PhysRevResearch.4.033212Mutual information for fermionic systemsLuca LeporiSimone PaganelliFabio FranchiniAndrea TrombettoniWe study the behavior of the mutual information (MI) in various quadratic fermionic chains, with and without pairing terms and both with short- and long-range hoppings. The models considered include the short-range limit and long-range versions of the Kitaev model as well, and also cases in which the area law for the entanglement entropy is—logarithmically or nonlogarithmically—violated. In all cases surveyed, when the area law is violated at most logarithmically, the MI is a monotonically increasing function of the conformal four-point ratio x. Where nonlogarithmic violations of the area law are present, nonmonotonic features can be observed in the MI, and the four-point ratio, as well as other natural combinations of the parameters, is found not to be sufficient to capture the whole structure of the MI with a collapse onto a single curve. We interpret this behavior as a sign that the structure of peaks is related to a nonuniversal spatial configuration of Bell pairs. For the model exhibiting a perfect volume law, the MI vanishes identically. For the Kitaev model the MI is vanishing for x→0 and it remains zero up to a finite x in the gapped case. In general, a larger range of the pairing corresponds to a reduction of the MI at small x. A discussion of the comparison with the results obtained by the anti–de Sitter/conformal field theory correspondence in the strong-coupling limit is presented.http://doi.org/10.1103/PhysRevResearch.4.033212 |
| spellingShingle | Luca Lepori Simone Paganelli Fabio Franchini Andrea Trombettoni Mutual information for fermionic systems Physical Review Research |
| title | Mutual information for fermionic systems |
| title_full | Mutual information for fermionic systems |
| title_fullStr | Mutual information for fermionic systems |
| title_full_unstemmed | Mutual information for fermionic systems |
| title_short | Mutual information for fermionic systems |
| title_sort | mutual information for fermionic systems |
| url | http://doi.org/10.1103/PhysRevResearch.4.033212 |
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