{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T19:11:13Z","timestamp":1790709073413,"version":"4.1.0"},"reference-count":69,"publisher":"American Physical Society (APS)","issue":"9","license":[{"start":{"date-parts":[[2025,3,6]],"date-time":"2025-03-06T00:00:00Z","timestamp":1741219200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100010661","name":"Horizon 2020 Framework Programme","doi-asserted-by":"publisher","award":["804213-TMCS"],"award-info":[{"award-number":["804213-TMCS"]}],"id":[{"id":"10.13039\/100010661","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. Lett."],"accepted":{"date-parts":[[2025,2,12]]},"abstract":"<jats:p>\n                    Continuous phase transitions where symmetry is spontaneously broken are ubiquitous in physics and often found between \u201cLandau-compatible\u201d phases where residual symmetries of one phase are a subset of the other. However, continuous \u201cdeconfined quantum critical\u201d transitions between Landau-incompatible symmetry-breaking phases are known to exist in certain quantum systems, often with anomalous microscopic symmetries. In this Letter, we investigate the need for such special conditions. We show that Landau-incompatible transitions can be found in a family of well-known classical statistical mechanical models with anomaly-free symmetries, introduced by Jos\u00e9  [.]. The models are anisotropic deformations of the classical 2D XY model labeled by a positive integer\n                    <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <a:mrow>\n                        <a:mi>Q<\/a:mi>\n                      <\/a:mrow>\n                    <\/a:math>\n                    . For a range of temperatures, even\n                    <c:math xmlns:c=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <c:mi>Q<\/c:mi>\n                    <\/c:math>\n                    models exhibit two Landau-incompatible partial symmetry-breaking phases and a direct transition between them for\n                    <e:math xmlns:e=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <e:mrow>\n                        <e:mi>Q<\/e:mi>\n                        <e:mo>\u2265<\/e:mo>\n                        <e:mn>4<\/e:mn>\n                      <\/e:mrow>\n                    <\/e:math>\n                    . Characteristic features of deconfined quantum criticality, such as enhanced symmetries and melting of charged defects, are easily seen in a classical setting. For odd\n                    <g:math xmlns:g=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <g:mrow>\n                        <g:mi>Q<\/g:mi>\n                      <\/g:mrow>\n                    <\/g:math>\n                    and corresponding temperature ranges, two regions of a single partial symmetry-breaking phase appear, split by a stable \u201cunnecessary critical\u201d line. We discuss experimental systems that realize these transitions and present anomaly-free quantum models that also exhibit similar phase diagrams.\n                  <\/jats:p>","DOI":"10.1103\/physrevlett.134.097103","type":"journal-article","created":{"date-parts":[[2025,3,6]],"date-time":"2025-03-06T10:02:32Z","timestamp":1741255352000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":7,"title":["Classical Origins of Landau-Incompatible Transitions"],"prefix":"10.1103","volume":"134","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8096-8596","authenticated-orcid":true,"given":"Abhishodh","family":"Prakash","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/052gg0110","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Oxford"},{"id":[{"id":"https:\/\/ror.org\/0165d9303","id-type":"ROR","asserted-by":"publisher"}],"name":"Harish-Chandra Research Institute"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0154-5358","authenticated-orcid":true,"given":"Nick G.","family":"Jones","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/052gg0110","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Oxford"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2025,3,6]]},"reference":[{"key":"PhysRevLett.134.097103Cc1R1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.93.25.14256","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc2R1","doi-asserted-by":"publisher","DOI":"10.1126\/science.1091806","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc3R1","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4916(61)90115-4","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc4R1","doi-asserted-by":"publisher","DOI":"10.1142\/9789811282386_0014","type":"book","volume-title":"50 Years of the Renormalization Group","author":"T. Senthil","year":"2024"},{"key":"PhysRevLett.134.097103Cc5R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.99.165143","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc6R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.99.205153","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc7R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.130.026801","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc8R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.107.155136","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc9R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.74.064405","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc10R1","doi-asserted-by":"publisher","DOI":"10.1103\/Physics.3.35","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc11R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.7.031051","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc12R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.98.085140","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc13R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.16.1217","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc14R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.9.021034","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc15R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.130.256401","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc16R1","unstructured":"See Supplemental Material at http:\/\/link.aps.org\/supplemental\/10.1103\/PhysRevLett.134.097103 for further information, including discussion of the phase diagrams and comments on anomalies, which includes Refs.\u00a0[17\u201331].","type":"other"},{"key":"PhysRevLett.134.097103Cc17R1","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(81)90049-9","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc18R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01224132","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc19R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.64.178","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc20R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.97.054412","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc21R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.96.195105","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc22R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.101.224437","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc23R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.119.127202","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc24R1","doi-asserted-by":"publisher","DOI":"10.21468\/SciPostPhys.15.2.051","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc25R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.111.087203","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc27R1","volume-title":"Quantum Phase Transitions","author":"S. Sachdev","year":"2009","type":"book"},{"key":"PhysRevLett.134.097103Cc28R1","volume-title":"Exactly Solved Models in Statistical Mechanics","author":"R.\u2009J. Baxter","year":"1982","type":"book"},{"key":"PhysRevLett.134.097103Cc29R1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-48487-7","type":"book","volume-title":"An Introduction to Integrable Techniques for One-Dimensional Quantum Systems","author":"F. Franchini","year":"2017"},{"key":"PhysRevLett.134.097103Cc30R1","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780198785781.003.0003","type":"book","volume-title":"Spin liquids and frustrated magnetism, Topological Aspects of Condensed Matter Physics","author":"J.\u2009T. Chalker","year":"2017"},{"key":"PhysRevLett.134.097103Cc32R1","doi-asserted-by":"publisher","DOI":"10.1016\/S0550-3213(02)00474-1","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc33R1","doi-asserted-by":"publisher","DOI":"10.1016\/S0550-3213(98)00063-7","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc34R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.11.041059","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc35R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.108.245135","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc36R1","doi-asserted-by":"publisher","DOI":"10.1051\/jphys:01975003606058100","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc37R1","volume-title":"Les Houches Summer School in Theoretical Physics: Fields, Strings, Critical Phenomena","author":"P.\u2009H. 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Fradkin","year":"2021","type":"book"},{"key":"PhysRevLett.134.097103Cc62R1","unstructured":"An analogous charge-binding transition and associated exotic critical phenomena in a 2d classical model were investigated in Refs.\u00a0[63, 64].","type":"other"},{"key":"PhysRevLett.134.097103Cc63R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.107.240601","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc64R1","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/aa89a1","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc65R1","unstructured":"The critical Ising model, which is the archetypal Landau-compatible transition, also has a mixed anomaly between the microscopic Ising symmetry and the emergent Kramers-Wannier symmetry\u00a0[66]. The key difference is that this mixed anomaly is explicitly broken by relevant operators, whereas the same is broken by irrelevant operators in our model.","type":"other"},{"key":"PhysRevLett.134.097103Cc67R1","unstructured":"Numerical evidence for a direct Landau-incompatible transition in an alternative classical model was presented in Ref.\u00a0[68].","type":"other"},{"key":"PhysRevLett.134.097103Cc68R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.108.075105","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc71R1","volume-title":"Talk at the Conference in Celebration of Dan Freed\u2019s 60th Birthday","author":"A. Kitaev","year":"2019","type":"conference-proceedings"},{"key":"PhysRevLett.134.097103Cc72R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.102.245113","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc73R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.108.125147","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc74R1","unstructured":"The identification by conjugation is often not stated in literature [75]. However, it is important for correct classification, and without it we would overcount the number of SSB phases. For Abelian groups, conjugation acts trivially, and various subgroups indeed represent distinct phases. For non-Abelian groups, this is not the case.","type":"other"},{"key":"PhysRevLett.134.097103Cc75R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.84.235128","type":"journal-article"},{"key":"PhysRevLett.134.097103Cc76R1","unstructured":"M. Hermele, Families of gapped systems and quantum pumps, Talk at Center for Mathematical Sciences and Applications (2021), www.youtube.com\/watch?v=wtaC0tqXZMU.","type":"other"}],"container-title":["Physical Review Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.aps.org\/article\/10.1103\/PhysRevLett.134.097103","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/harvest.aps.org\/v2\/journals\/articles\/10.1103\/PhysRevLett.134.097103\/fulltext","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T18:45:47Z","timestamp":1790707547000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.aps.org\/doi\/10.1103\/PhysRevLett.134.097103"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,6]]},"references-count":69,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2025,3]]}},"URL":"https:\/\/doi.org\/10.1103\/physrevlett.134.097103","relation":{"has-preprint":[{"id-type":"doi","id":"10.48550\/arXiv.2404.19009","asserted-by":"subject"}]},"ISSN":["0031-9007","1079-7114"],"issn-type":[{"value":"0031-9007","type":"print"},{"value":"1079-7114","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,6]]},"assertion":[{"value":"2024-06-15","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"Published by the American Physical Society. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2025","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/","name":"creative_commons_license","label":"Creative Commons license","group":{"name":"licenses","label":"Licenses"}},{"value":"\u00a92025 The authors","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"097103"}}