{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T03:24:36Z","timestamp":1773890676761,"version":"3.50.1"},"reference-count":40,"publisher":"American Physical Society (APS)","issue":"4","license":[{"start":{"date-parts":[[2024,1,31]],"date-time":"2024-01-31T00:00:00Z","timestamp":1706659200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000275","name":"Leverhulme Trust","doi-asserted-by":"publisher","award":["LIP-202-014"],"award-info":[{"award-number":["LIP-202-014"]}],"id":[{"id":"10.13039\/501100000275","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["NSF PHY-1748958"],"award-info":[{"award-number":["NSF PHY-1748958"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. B"],"accepted":{"date-parts":[[2024,1,4]]},"abstract":"<jats:p>We consider electronic systems with a spontaneously broken continuous symmetry. The scattering vertex between electrons and Goldstone modes is calculated over the entire Brillouin zone using the random phase approximation. This calculation reveals two things: (1) electrons always couple to both <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><a:mi>\u03d5<\/a:mi><\/a:math> and <b:math xmlns:b=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><b:mrow><b:msub><b:mi>\u2202<\/b:mi><b:mi>t<\/b:mi><\/b:msub><b:mi>\u03d5<\/b:mi><\/b:mrow><\/b:math>, where <c:math xmlns:c=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><c:mi>\u03d5<\/c:mi><\/c:math> is the Goldstone field, and (2) quasiparticles in a state with continuous symmetry breaking have to be defined in a rotating frame, which locally follows the fluctuations of the order parameter. The implications of these findings for electron spectral functions in both symmetry-broken and thermally disordered systems are discussed, and the examples of antiferromagnetism in the Hubbard model and spin spiral order in the three-band model are worked out in detail.<\/jats:p>\n          <jats:sec>\n            <jats:title\/>\n            <jats:supplementary-material>\n              <jats:permissions>\n                <jats:copyright-statement>Published by the American Physical Society<\/jats:copyright-statement>\n                <jats:copyright-year>2024<\/jats:copyright-year>\n              <\/jats:permissions>\n            <\/jats:supplementary-material>\n          <\/jats:sec>","DOI":"10.1103\/physrevb.109.045155","type":"journal-article","created":{"date-parts":[[2024,1,31]],"date-time":"2024-01-31T15:07:11Z","timestamp":1706713631000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":5,"title":["Electrons interacting with Goldstone modes and the rotating frame"],"prefix":"10.1103","volume":"109","author":[{"given":"Konstantinos","family":"Vasiliou","sequence":"first","affiliation":[{"name":"Rudolf Peierls Centre for Theoretical Physics, Parks Road, Oxford OX1 3PU, United Kingdom"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3335-2398","authenticated-orcid":true,"given":"Yuchi","family":"He","sequence":"additional","affiliation":[{"name":"Rudolf Peierls Centre for Theoretical Physics, Parks Road, Oxford OX1 3PU, United Kingdom"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2781-4085","authenticated-orcid":true,"given":"Nick","family":"Bultinck","sequence":"additional","affiliation":[{"name":"Rudolf Peierls Centre for Theoretical Physics, Parks Road, Oxford OX1 3PU, United Kingdom"},{"name":"Department of Physics, Ghent University, Krijgslaan 281, 9000 Gent, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"16","published-online":{"date-parts":[[2024,1,31]]},"reference":[{"key":"PhysRevB.109.045155Cc1R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.124.287"},{"key":"PhysRevB.109.045155Cc2R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02726371"},{"key":"PhysRevB.109.045155Cc3R1","doi-asserted-by":"crossref","DOI":"10.1007\/3-540-10579-4","volume-title":"Geometry of the Time-dependent Variational Principle in Quantum Mechanics","author":"P. 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