{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T17:05:12Z","timestamp":1790701512328,"version":"4.1.0"},"reference-count":73,"publisher":"National Academy of Sciences","issue":"40","license":[{"start":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T00:00:00Z","timestamp":1790640000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"MOST | National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2022YFA1402702"],"award-info":[{"award-number":["2022YFA1402702"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"MOST | National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2021YFA1401400"],"award-info":[{"award-number":["2021YFA1401400"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"MOST | National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12447103"],"award-info":[{"award-number":["12447103"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"MOST | National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12274289"],"award-info":[{"award-number":["12274289"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Innovation Program for Quantum Science and Technology","award":["2021ZD0301902"],"award-info":[{"award-number":["2021ZD0301902"]}]},{"name":"Yangyang Development Fund","award":["-"],"award-info":[{"award-number":["-"]}]},{"name":"Shanghai Jiao Tong University 2030 Initiative","award":["-"],"award-info":[{"award-number":["-"]}],"id":[{"id":"https:\/\/ror.org\/0220qvk04","id-type":"ROR","asserted-by":"crossref"}]},{"name":"startup funds from SJTU","award":["-"],"award-info":[{"award-number":["-"]}]},{"name":"T. D. Lee scholarship","award":["-"],"award-info":[{"award-number":["-"]}]},{"DOI":"10.13039\/501100001809","name":"MOST | National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["125B2077"],"award-info":[{"award-number":["125B2077"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2026,10,6]]},"abstract":"<jats:p>\n                    Characterizing mixed-state entanglement in fermionic quantum matter represents a fundamental challenge at the intersection of condensed matter physics and quantum information. Unlike pure states, mixed states lack a universally accepted and easily computable entanglement measure, a difficulty compounded in fermionic systems by the ambiguity of the partial transpose operation. Here, motivated by the Hermiticity of the partially transposed density matrix and the analytic continuation of the R\u00e9nyi negativity to logarithmic negativity, we address this puzzle by demonstrating the \u201ctwisted\u201d R\u00e9nyi negativity as a physically consistent proxy for mixed-state entanglement in the Hubbard and spinless\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:mi>t<\/mml:mi>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    -\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:mi>V<\/mml:mi>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    models. Through large-scale quantum Monte Carlo simulations of these paradigmatic correlated systems, we show that this indicator captures essential physical expectations\u2014including the area law and monotonic thermal suppression\u2014while excluding anomalous behavior present in alternative definitions. Our findings not only provide a robust theoretical framework for quantifying entanglement in strongly correlated electronic systems but also offer a practical tool for experimental detection in rapidly developing platforms, including ultracold atomic gases and programmable quantum simulators.\n                  <\/jats:p>","DOI":"10.1073\/pnas.2534602123","type":"journal-article","created":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T16:18:26Z","timestamp":1790698706000},"update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":0,"title":["Twisted R\u00e9nyi negativity as a reliable proxy for mixed-state entanglement in fermionic systems"],"prefix":"10.1073","volume":"123","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-2185-1961","authenticated-orcid":false,"given":"Fo-Hong","family":"Wang","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/0220qvk04","id-type":"ROR","asserted-by":"publisher"}],"name":"Tsung-Dao Lee Institute, Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), School of Physics and Astronomy, Shanghai Jiao Tong University","place":["Shanghai, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8615-7396","authenticated-orcid":false,"given":"Xiao Yan","family":"Xu","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/0220qvk04","id-type":"ROR","asserted-by":"publisher"}],"name":"Tsung-Dao Lee Institute, Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), School of Physics and Astronomy, Shanghai Jiao Tong University","place":["Shanghai, China"]},{"name":"Hefei National Laboratory","place":["Hefei, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"341","published-online":{"date-parts":[[2026,9,29]]},"reference":[{"key":"e_1_3_4_1_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.90.227902"},{"key":"e_1_3_4_2_2","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.80.517"},{"key":"e_1_3_4_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2016.06.008"},{"key":"e_1_3_4_4_2","first-page":"1","article-title":"An introduction to entanglement measures","volume":"7","author":"Plenio M. B.","year":"2007","unstructured":"M. B. Plenio, S. Virmani, An introduction to entanglement measures. Quantum Inf. Comput. 7, 1\u201351 (2007).","journal-title":"Quantum Inf. Comput."},{"key":"e_1_3_4_5_2","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.81.865"},{"key":"e_1_3_4_6_2","doi-asserted-by":"crossref","first-page":"P06002","DOI":"10.1088\/1742-5468\/2004\/06\/P06002","article-title":"Entanglement entropy and quantum field theory","volume":"2004","author":"Calabrese P.","year":"2004","unstructured":"P. Calabrese, J. Cardy, Entanglement entropy and quantum field theory. J. Stat. Mech. Theory Exp. 2004, P06002 (2004).","journal-title":"J. Stat. Mech. 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Meng The teaching from entanglement: 2D SU(2) antiferromagnet to valence bond solid deconfined quantum critical points are not conformal. arXiv [Preprint] (2023). https:\/\/doi.org\/10.48550\/arXiv.2302.11742 (Accessed 14 September 2026)."},{"key":"e_1_3_4_59_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.109.205147"},{"key":"e_1_3_4_60_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008923215028"},{"key":"e_1_3_4_61_2","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/10\/6\/065001"},{"key":"e_1_3_4_62_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.95.062132"},{"key":"e_1_3_4_63_2","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP06(2023)030"},{"key":"e_1_3_4_64_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.111.L081108"},{"key":"e_1_3_4_65_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.110.165152"},{"key":"e_1_3_4_66_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.32.103"},{"key":"e_1_3_4_67_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-025-57971-8"},{"key":"e_1_3_4_68_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.2.043345"},{"key":"e_1_3_4_69_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.88.155103"},{"key":"e_1_3_4_70_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.106.135701"},{"key":"e_1_3_4_71_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.87.195134"},{"key":"e_1_3_4_72_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.113.110401"},{"key":"e_1_3_4_73_2","unstructured":"F.-H. Wang X. Y. Xu Raw data for \u201cTwisted R\u00e9nyi negativity as a reliable proxy for mixed-state entanglement in fermionic systems.\u201d Shanghai Jiao Tong University Scidata. https:\/\/scidata.sjtu.edu.cn\/records\/jv4rn-yk209. Deposited 12 September 2026."}],"container-title":["Proceedings of the National Academy of Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pnas.org\/doi\/pdf\/10.1073\/pnas.2534602123","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T16:19:22Z","timestamp":1790698762000},"score":1,"resource":{"primary":{"URL":"https:\/\/pnas.org\/doi\/10.1073\/pnas.2534602123"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,29]]},"references-count":73,"journal-issue":{"issue":"40","published-print":{"date-parts":[[2026,10,6]]}},"alternative-id":["10.1073\/pnas.2534602123"],"URL":"https:\/\/doi.org\/10.1073\/pnas.2534602123","relation":{},"ISSN":["0027-8424","1091-6490"],"issn-type":[{"value":"0027-8424","type":"print"},{"value":"1091-6490","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,29]]},"assertion":[{"value":"2025-11-28","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-08-28","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-09-29","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e2534602123"}}