Duality between weak and strong interactions in quantum gases
In one-dimensional quantum gases there is a well known “duality” between hard core bosons and noninteracting fermions. However, at the field theory level, no exact duality connecting strongly interacting bosons to weakly interacting fermions is known. Here we propose a solution to this long-standing...
| Main Authors: | , , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
American Physical Society
2022
|
| _version_ | 1797101173739618304 |
|---|---|
| author | Granet, E Bertini, B Essler, FHL |
| author_facet | Granet, E Bertini, B Essler, FHL |
| author_sort | Granet, E |
| collection | OXFORD |
| description | In one-dimensional quantum gases there is a well known “duality” between hard core bosons and noninteracting fermions. However, at the field theory level, no exact duality connecting strongly interacting bosons to weakly interacting fermions is known. Here we propose a solution to this long-standing problem. Our derivation relies on regularizing the only pointlike interaction between fermions in one dimension that induces a discontinuity in the wave function proportional to its derivative. In contrast to all known regularizations our potential is weak for small interaction strengths. Crucially, this allows one to apply standard methods of diagrammatic perturbation theory to strongly interacting bosons. As a first application we compute the finite temperature spectral function of the Cheon-Shigehara model, the fermionic model dual to the celebrated Lieb-Liniger model. |
| first_indexed | 2024-03-07T05:48:04Z |
| format | Journal article |
| id | oxford-uuid:e7e5517b-344e-489d-8d5c-10d0895fe580 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:48:04Z |
| publishDate | 2022 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | oxford-uuid:e7e5517b-344e-489d-8d5c-10d0895fe5802022-03-27T10:42:31ZDuality between weak and strong interactions in quantum gasesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e7e5517b-344e-489d-8d5c-10d0895fe580EnglishSymplectic ElementsAmerican Physical Society2022Granet, EBertini, BEssler, FHLIn one-dimensional quantum gases there is a well known “duality” between hard core bosons and noninteracting fermions. However, at the field theory level, no exact duality connecting strongly interacting bosons to weakly interacting fermions is known. Here we propose a solution to this long-standing problem. Our derivation relies on regularizing the only pointlike interaction between fermions in one dimension that induces a discontinuity in the wave function proportional to its derivative. In contrast to all known regularizations our potential is weak for small interaction strengths. Crucially, this allows one to apply standard methods of diagrammatic perturbation theory to strongly interacting bosons. As a first application we compute the finite temperature spectral function of the Cheon-Shigehara model, the fermionic model dual to the celebrated Lieb-Liniger model. |
| spellingShingle | Granet, E Bertini, B Essler, FHL Duality between weak and strong interactions in quantum gases |
| title | Duality between weak and strong interactions in quantum gases |
| title_full | Duality between weak and strong interactions in quantum gases |
| title_fullStr | Duality between weak and strong interactions in quantum gases |
| title_full_unstemmed | Duality between weak and strong interactions in quantum gases |
| title_short | Duality between weak and strong interactions in quantum gases |
| title_sort | duality between weak and strong interactions in quantum gases |
| work_keys_str_mv | AT granete dualitybetweenweakandstronginteractionsinquantumgases AT bertinib dualitybetweenweakandstronginteractionsinquantumgases AT esslerfhl dualitybetweenweakandstronginteractionsinquantumgases |