Inferring effective field observables from a discrete model
A spin system on a lattice can usually be modeled at large scales by an effective quantum field theory. A key mathematical result relating the two descriptions is the quantum central limit theorem, which shows that certain spin observables satisfy an algebra of bosonic fields under certain condition...
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| Format: | Article |
| Language: | English |
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IOP Publishing
2017-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/19/1/013013 |
| _version_ | 1797750903418126336 |
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| author | Cédric Bény |
| author_facet | Cédric Bény |
| author_sort | Cédric Bény |
| collection | DOAJ |
| description | A spin system on a lattice can usually be modeled at large scales by an effective quantum field theory. A key mathematical result relating the two descriptions is the quantum central limit theorem, which shows that certain spin observables satisfy an algebra of bosonic fields under certain conditions. Here, we show that these particular observables and conditions are the relevant ones for an observer with certain limited abilities to resolve spatial locations as well as spin values. This is shown by computing the asymptotic behaviour of a quantum Fisher information metric as function of the resolution parameters. The relevant observables characterise the state perturbations whose distinguishability does not decay too fast as a function of spatial or spin resolution. |
| first_indexed | 2024-03-12T16:40:37Z |
| format | Article |
| id | doaj.art-8b6d4aecc7fb45a58ae3faf71a34881d |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:40:37Z |
| publishDate | 2017-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-8b6d4aecc7fb45a58ae3faf71a34881d2023-08-08T14:33:33ZengIOP PublishingNew Journal of Physics1367-26302017-01-0119101301310.1088/1367-2630/19/1/013013Inferring effective field observables from a discrete modelCédric Bény0Institut für Theoretische Physik, Leibniz Universität Hannover , Appelstraße 2, D-30167 Hannover, Germany; Department of Applied Mathematics, Hanyang University (ERICA) , 55 Hanyangdaehak-ro, Ansan, Gyeonggi-do, 426-791, KoreaA spin system on a lattice can usually be modeled at large scales by an effective quantum field theory. A key mathematical result relating the two descriptions is the quantum central limit theorem, which shows that certain spin observables satisfy an algebra of bosonic fields under certain conditions. Here, we show that these particular observables and conditions are the relevant ones for an observer with certain limited abilities to resolve spatial locations as well as spin values. This is shown by computing the asymptotic behaviour of a quantum Fisher information metric as function of the resolution parameters. The relevant observables characterise the state perturbations whose distinguishability does not decay too fast as a function of spatial or spin resolution.https://doi.org/10.1088/1367-2630/19/1/013013Fisher information metriccentral limit theoremquantum informationquantum field theory |
| spellingShingle | Cédric Bény Inferring effective field observables from a discrete model New Journal of Physics Fisher information metric central limit theorem quantum information quantum field theory |
| title | Inferring effective field observables from a discrete model |
| title_full | Inferring effective field observables from a discrete model |
| title_fullStr | Inferring effective field observables from a discrete model |
| title_full_unstemmed | Inferring effective field observables from a discrete model |
| title_short | Inferring effective field observables from a discrete model |
| title_sort | inferring effective field observables from a discrete model |
| topic | Fisher information metric central limit theorem quantum information quantum field theory |
| url | https://doi.org/10.1088/1367-2630/19/1/013013 |
| work_keys_str_mv | AT cedricbeny inferringeffectivefieldobservablesfromadiscretemodel |