{"id":"https://openalex.org/W7172480366","doi":"https://doi.org/10.1103/rbrl-6shw","title":"Phase diagram of the Kitaev-Heisenberg- \u0393 model: Classical and quantum magnetism, frustration, and subdominant interactions","display_name":"Phase diagram of the Kitaev-Heisenberg- \u0393 model: Classical and quantum magnetism, frustration, and subdominant interactions","publication_year":2026,"publication_date":"2026-08-05","ids":{"openalex":"https://openalex.org/W7172480366","doi":"https://doi.org/10.1103/rbrl-6shw"},"language":"en","primary_location":{"id":"doi:10.1103/rbrl-6shw","doi":"https://doi.org/10.1103/rbrl-6shw","is_oa":false,"landing_page_url":"https://doi.org/10.1103/rbrl-6shw","pdf_url":null,"source":{"id":"https://openalex.org/S4210237713","display_name":"Physical review. B./Physical review. B","issn_l":"2469-9950","issn":["2469-9950","2469-9969","2469-9977"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-a","jufo-2","norway-2","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review B","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2606.13263","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5144444845","display_name":"Anonymous","orcid":"https://orcid.org/0000-0001-9782-4708","observed_orcids":["https://orcid.org/0000-0001-9782-4708","https://orcid.org/0000-0002-0030-8326","https://orcid.org/0000-0002-1664-5925","https://orcid.org/0000-0002-2360-6027","https://orcid.org/0000-0002-4695-4059","https://orcid.org/0000-0002-5787-5022","https://orcid.org/0000-0002-9583-3640","https://orcid.org/0009-0000-2840-3491","https://orcid.org/0009-0001-6787-4824","https://orcid.org/0009-0006-9863-1741","https://orcid.org/0009-0008-6646-1391","https://orcid.org/0009-0009-7363-2184"]},"institutions":[{"id":"https://openalex.org/I135768898","display_name":"Ritsumeikan University","ror":"https://ror.org/0197nmd03","country_code":"JP","type":"education","lineage":["https://openalex.org/I135768898","https://openalex.org/I4390039241"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kiyu Fukui","raw_affiliation_strings":["Ritsumeikan University"],"raw_orcid":"https://orcid.org/0000-0002-1664-5925","affiliations":[{"raw_affiliation_string":"Ritsumeikan University","institution_ids":["https://openalex.org/I135768898"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003493165","display_name":"Yukitoshi Motome","orcid":"https://orcid.org/0000-0003-0707-366X","observed_orcids":["https://orcid.org/0000-0003-0707-366X"]},"institutions":[{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yukitoshi Motome","raw_affiliation_strings":["The University of Tokyo"],"raw_orcid":"https://orcid.org/0000-0003-0707-366X","affiliations":[{"raw_affiliation_string":"The University of Tokyo","institution_ids":["https://openalex.org/I74801974"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.42575323,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"114","issue":"7","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11682","display_name":"Advanced Condensed Matter Physics","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11682","display_name":"Advanced Condensed Matter Physics","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10037","display_name":"Physics of Superconductivity and Magnetism","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/kitaev-spin-liquid","display_name":"Kitaev spin liquid","score":0.9419999718666077},{"id":"https://openalex.org/keywords/ground-state-phase-diagram","display_name":"ground-state phase diagram","score":0.9070000052452087},{"id":"https://openalex.org/keywords/noncollinear-magnetic-order","display_name":"noncollinear magnetic order","score":0.7680000066757202},{"id":"https://openalex.org/keywords/incommensurate-magnetic-order","display_name":"incommensurate magnetic order","score":0.7440000176429749},{"id":"https://openalex.org/keywords/quantum-fluctuations","display_name":"quantum fluctuations","score":0.7310000061988831},{"id":"https://openalex.org/keywords/magnetic-frustration","display_name":"frustrated magnetism","score":0.8360000252723694},{"id":"https://openalex.org/keywords/quantum-spin-liquid","display_name":"quantum spin liquid","score":0.4790000021457672}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6832000017166138},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4754999876022339},{"id":"https://openalex.org/C2778886782","wikidata":"https://www.wikidata.org/wiki/Q536541","display_name":"Subdominant","level":4,"score":0.46619999408721924},{"id":"https://openalex.org/C85906118","wikidata":"https://www.wikidata.org/wiki/Q186693","display_name":"Phase diagram","level":3,"score":0.45719999074935913},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3828999996185303},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.3813000023365021},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3276999890804291},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.30660000443458557},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.30480000376701355},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.3003000020980835},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.2921999990940094},{"id":"https://openalex.org/C141886431","wikidata":"https://www.wikidata.org/wiki/Q1193821","display_name":"Quantum fluctuation","level":3,"score":0.28130000829696655},{"id":"https://openalex.org/C3079626","wikidata":"https://www.wikidata.org/wiki/Q234881","display_name":"Quantum electrodynamics","level":1,"score":0.2759000062942505},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.2754000127315521},{"id":"https://openalex.org/C52233224","wikidata":"https://www.wikidata.org/wiki/Q44363","display_name":"Fermion","level":2,"score":0.26989999413490295},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.262800008058548}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1103/rbrl-6shw","doi":"https://doi.org/10.1103/rbrl-6shw","is_oa":false,"landing_page_url":"https://doi.org/10.1103/rbrl-6shw","pdf_url":null,"source":{"id":"https://openalex.org/S4210237713","display_name":"Physical review. B./Physical review. B","issn_l":"2469-9950","issn":["2469-9950","2469-9969","2469-9977"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-a","jufo-2","norway-2","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review B","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2606.13263","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2606.13263","pdf_url":"https://arxiv.org/pdf/2606.13263","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2606.13263","doi":"https://doi.org/10.48550/arxiv.2606.13263","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.13263","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2606.13263","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2606.13263","pdf_url":"https://arxiv.org/pdf/2606.13263","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G440403301","display_name":"Exploring Quantum Spin Liquids in Rare-Earth Magnetic Materials","funder_award_id":"26H02011","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G5773010482","display_name":null,"funder_award_id":"JP25H01247","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G6080884103","display_name":"Elucidating the effects of dissipation on creation, detection, and manipulation of non-Abelian quasiparticles in quantum spin liquids","funder_award_id":"24K17009","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G8520042547","display_name":"Creation and control of Majorana particles in quantum spin liquids","funder_award_id":"20H00122","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320323954","display_name":"University of Tsukuba","ror":"https://ror.org/02956yf07"},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7172480366.pdf","grobid_xml":"https://content.openalex.org/works/W7172480366.grobid-xml"},"referenced_works_count":144,"referenced_works":["https://openalex.org/W110583329","https://openalex.org/W596821666","https://openalex.org/W1531472254","https://openalex.org/W1546895923","https://openalex.org/W1593038823","https://openalex.org/W1703930556","https://openalex.org/W1746157392","https://openalex.org/W1756204588","https://openalex.org/W1827528477","https://openalex.org/W1874324710","https://openalex.org/W1966808325","https://openalex.org/W1968417812","https://openalex.org/W1975313068","https://openalex.org/W1980743096","https://openalex.org/W1988443731","https://openalex.org/W1988974121","https://openalex.org/W1991736153","https://openalex.org/W1993390203","https://openalex.org/W2002786054","https://openalex.org/W2009820981","https://openalex.org/W2029100014","https://openalex.org/W2035868209","https://openalex.org/W2044506218","https://openalex.org/W2048639010","https://openalex.org/W2049126606","https://openalex.org/W2054661952","https://openalex.org/W2058698561","https://openalex.org/W2064230874","https://openalex.org/W2065719463","https://openalex.org/W2069589318","https://openalex.org/W2091393784","https://openalex.org/W2092134000","https://openalex.org/W2106339652","https://openalex.org/W2122266271","https://openalex.org/W2130585357","https://openalex.org/W2135273380","https://openalex.org/W2141708961","https://openalex.org/W2152240519","https://openalex.org/W2161612867","https://openalex.org/W2256298911","https://openalex.org/W2274556558","https://openalex.org/W2276166310","https://openalex.org/W2293879704","https://openalex.org/W2322298429","https://openalex.org/W2340523190","https://openalex.org/W2479153330","https://openalex.org/W2510898798","https://openalex.org/W2513548694","https://openalex.org/W2515000701","https://openalex.org/W2541044129","https://openalex.org/W2577242602","https://openalex.org/W2631568866","https://openalex.org/W2726673580","https://openalex.org/W2765799776","https://openalex.org/W2766685321","https://openalex.org/W2783319045","https://openalex.org/W2786908670","https://openalex.org/W2791819056","https://openalex.org/W2800494476","https://openalex.org/W2804288288","https://openalex.org/W2810275113","https://openalex.org/W2912539264","https://openalex.org/W2914340208","https://openalex.org/W2918156786","https://openalex.org/W2922583464","https://openalex.org/W2922621522","https://openalex.org/W2943948900","https://openalex.org/W2946164685","https://openalex.org/W2947969665","https://openalex.org/W2962821121","https://openalex.org/W2963047621","https://openalex.org/W2969954741","https://openalex.org/W2975873088","https://openalex.org/W2976073046","https://openalex.org/W2991673639","https://openalex.org/W2999433068","https://openalex.org/W3000212067","https://openalex.org/W3005771755","https://openalex.org/W3007005547","https://openalex.org/W3012202344","https://openalex.org/W3013647672","https://openalex.org/W3020028056","https://openalex.org/W3022796749","https://openalex.org/W3023751024","https://openalex.org/W3042532473","https://openalex.org/W3043535183","https://openalex.org/W3084352519","https://openalex.org/W3093218017","https://openalex.org/W3096759255","https://openalex.org/W3100763970","https://openalex.org/W3105759879","https://openalex.org/W3111351075","https://openalex.org/W3118135232","https://openalex.org/W3118429772","https://openalex.org/W3124692788","https://openalex.org/W3127468591","https://openalex.org/W3173089686","https://openalex.org/W3187851860","https://openalex.org/W3199526042","https://openalex.org/W3201534105","https://openalex.org/W3205049350","https://openalex.org/W3209923266","https://openalex.org/W3213420774","https://openalex.org/W3213565322","https://openalex.org/W3215846046","https://openalex.org/W4206180194","https://openalex.org/W4210323352","https://openalex.org/W4213230748","https://openalex.org/W4225697302","https://openalex.org/W4255179177","https://openalex.org/W4255243486","https://openalex.org/W4281877819","https://openalex.org/W4292622292","https://openalex.org/W4293463477","https://openalex.org/W4309326496","https://openalex.org/W4309660460","https://openalex.org/W4310810772","https://openalex.org/W4313622215","https://openalex.org/W4317861037","https://openalex.org/W4362600731","https://openalex.org/W4379231480","https://openalex.org/W4387378266","https://openalex.org/W4388825125","https://openalex.org/W4390006356","https://openalex.org/W4391015254","https://openalex.org/W4391015274","https://openalex.org/W4392284713","https://openalex.org/W4392778913","https://openalex.org/W4400733159","https://openalex.org/W4401443509","https://openalex.org/W4402632502","https://openalex.org/W4404346242","https://openalex.org/W4404992850","https://openalex.org/W4406668367","https://openalex.org/W4407682460","https://openalex.org/W4410435896","https://openalex.org/W4412427477","https://openalex.org/W4413927840","https://openalex.org/W4416971567","https://openalex.org/W4417128643","https://openalex.org/W4417209549","https://openalex.org/W6926960497","https://openalex.org/W7134896647","https://openalex.org/W7136870688"],"related_works":["https://openalex.org/W2510898798","https://openalex.org/W2886992638","https://openalex.org/W4404992850","https://openalex.org/W3017526446","https://openalex.org/W3080854677","https://openalex.org/W4388032362","https://openalex.org/W2913089378","https://openalex.org/W3213259200","https://openalex.org/W3186934928","https://openalex.org/W4284707755"],"abstract_inverted_index":{"The":[0],"Kitaev":[1,35,74,223],"spin":[2,12,75,164,224],"liquid":[3,13,76,165],"provides":[4],"a":[5,24,108,114,149,185,200],"rare":[6],"example":[7],"of":[8,26,73,88,116,138,152],"exactly":[9],"solvable":[10],"quantum":[11,96,129,134,196],"states.":[14],"Intensive":[15],"research":[16],"over":[17],"the":[18,34,46,68,84,89,103,128,139,144,189,222],"past":[19],"two":[20],"decades":[21],"has":[22],"identified":[23],"variety":[25,115],"its":[27],"candidate":[28,77,210],"materials.":[29,78],"In":[30,79,102,127],"real":[31],"materials,":[32,211],"however,":[33],"interaction":[36],"is":[37],"inevitably":[38],"accompanied":[39],"by":[40,177],"additional":[41,179],"magnetic":[42,55,119,180],"interactions":[43,52],"such":[44],"as":[45,167,169],"Heisenberg":[47],"and":[48,71,95,122,195,198,216],"$\u0393$":[49],"interactions.":[50,181],"These":[51],"often":[53],"induce":[54],"ordering":[56],"at":[57],"low":[58],"temperatures,":[59],"making":[60],"it":[61],"essential":[62],"to":[63,220],"clarify":[64],"their":[65],"effects":[66],"in":[67,143,148],"search":[69],"for":[70,192,205,214],"design":[72],"this":[80],"study,":[81],"we":[82,106,131],"revisit":[83],"ground-state":[85],"phase":[86],"diagram":[87],"Kitaev-Heisenberg-$\u0393$":[90,190],"model":[91,191],"from":[92],"both":[93,193],"classical":[94,104,145,194],"perspectives,":[97],"using":[98],"state-of-the-art":[99],"numerical":[100],"techniques.":[101],"case,":[105,130,146],"reveal":[107],"$zoo$":[109],"$of$":[110],"$noncollinear$":[111],"$orders$,":[112],"where":[113,162],"noncollinear":[117],"multiple-$Q$":[118],"orders":[120,141],"with":[121],"without":[123],"incommensurate":[124,154],"modulations":[125],"emerge.":[126],"unravel":[132],"that":[133],"fluctuations":[135],"suppress":[136],"many":[137],"competing":[140],"found":[142],"resulting":[147],"reduced":[150],"number":[151],"dominant":[153],"orders.":[155],"We":[156],"further":[157],"identify":[158],"$highly$":[159],"$frustrated$":[160],"regions,":[161],"spiral":[163],"states":[166,173],"well":[168],"new":[170,218],"magnetically":[171],"ordered":[172],"are":[174],"potentially":[175],"stabilized":[176],"other":[178],"Our":[182],"results":[183,208],"provide":[184],"comprehensive":[186],"perspective":[187],"on":[188,209],"spins":[197],"offer":[199],"valuable":[201],"guide":[202],"not":[203],"only":[204],"interpreting":[206],"experimental":[207],"but":[212],"also":[213],"searching":[215],"designing":[217],"materials":[219],"realize":[221],"liquid.":[225]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-08-06T00:00:00"}