{"id":"https://openalex.org/W7214804402","doi":"https://doi.org/10.48550/arxiv.2609.33454","title":"Kitaev-Heisenberg model on the square-hexagon-dodecagon lattice","display_name":"Kitaev-Heisenberg model on the square-hexagon-dodecagon lattice","publication_year":2026,"publication_date":"2026-09-27","ids":{"openalex":"https://openalex.org/W7214804402","doi":"https://doi.org/10.48550/arxiv.2609.33454"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.33454","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33454","pdf_url":"https://arxiv.org/pdf/2609.33454","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.33454","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016965726","display_name":"\u0633\u0639\u06cc\u062f \u0628\u0631\u0627\u0631\u06cc","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I161028277","display_name":"Institute for Advanced Studies in Basic Sciences","ror":"https://ror.org/00bzsst90","country_code":"IR","type":"education","lineage":["https://openalex.org/I161028277"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Barari, Saeed","raw_affiliation_strings":["Department of Physics , Institute for Advanced Studies in Basic Sciences (IASBS) , Zanjan 45137-66731 , Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics , Institute for Advanced Studies in Basic Sciences (IASBS) , Zanjan 45137-66731 , Iran","institution_ids":["https://openalex.org/I161028277"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072782132","display_name":"Yasir Iqbal","orcid":"https://orcid.org/0000-0002-3387-0120","observed_orcids":["https://orcid.org/0000-0002-3387-0120","https://orcid.org/0000-0003-0936-8947"]},"institutions":[{"id":"https://openalex.org/I24676775","display_name":"Indian Institute of Technology Madras","ror":"https://ror.org/03v0r5n49","country_code":"IN","type":"education","lineage":["https://openalex.org/I24676775"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Iqbal, Yasir","raw_affiliation_strings":["Department of Physics , Indian Institute of Technology Madras , Chennai 600036 , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics , Indian Institute of Technology Madras , Chennai 600036 , India","institution_ids":["https://openalex.org/I24676775"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061856403","display_name":"G. Baskaran","orcid":"https://orcid.org/0009-0009-5870-4442","observed_orcids":["https://orcid.org/0009-0009-5870-4442"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Baskaran, Ganapathy","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059974749","display_name":"Saeed S. Jahromi","orcid":"https://orcid.org/0000-0001-7994-8192","observed_orcids":["https://orcid.org/0000-0001-7994-8192"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jahromi, Saeed S.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100386371","display_name":"Chunxiao Liu","orcid":"https://orcid.org/0000-0002-0695-1291","observed_orcids":["https://orcid.org/0000-0002-0695-1291"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]},{"id":"https://openalex.org/I2799857465","display_name":"Laboratoire de physique des Solides","ror":"https://ror.org/02dyaew97","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I2799857465"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Liu, Chunxiao","raw_affiliation_strings":["Universit\u00e9 Paris-Saclay , CNRS , Laboratoire de Physique des Solides , 91405 Orsay , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Paris-Saclay , CNRS , Laboratoire de Physique des Solides , 91405 Orsay , France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I2799857465"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030014432","display_name":"Julien Vidal","orcid":"https://orcid.org/0000-0002-1788-643X","observed_orcids":["https://orcid.org/0000-0002-1788-643X"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I24676775","display_name":"Indian Institute of Technology Madras","ror":"https://ror.org/03v0r5n49","country_code":"IN","type":"education","lineage":["https://openalex.org/I24676775"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210140797","display_name":"Laboratoire de Physique Th\u00e9orique de la Mati\u00e8re Condens\u00e9e","ror":"https://ror.org/04zaaa143","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I39804081","https://openalex.org/I4210098836","https://openalex.org/I4210140797"]}],"countries":["FR","IN"],"is_corresponding":false,"raw_author_name":"Vidal, Julien","raw_affiliation_strings":["Department of Physics , Indian Institute of Technology Madras , Chennai 600036 , India","Sorbonne Universit\u00e9 , CNRS , Laboratoire de Physique Th\u00e9orique de la Mati\u00e8re Condens\u00e9e , LPTMC , F-75005 Paris , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics , Indian Institute of Technology Madras , Chennai 600036 , India","institution_ids":["https://openalex.org/I24676775"]},{"raw_affiliation_string":"Sorbonne Universit\u00e9 , CNRS , Laboratoire de Physique Th\u00e9orique de la Mati\u00e8re Condens\u00e9e , LPTMC , F-75005 Paris , France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I39804081","https://openalex.org/I4210140797"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":7,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.9315999746322632,"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":0.9315999746322632,"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/T11804","display_name":"Quantum many-body systems","score":0.052299998700618744,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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":0.0035000001080334187,"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-heisenberg-model","display_name":"Kitaev-Heisenberg model","score":1.0},{"id":"https://openalex.org/keywords/spin-1-2-systems","display_name":"spin-1/2 systems","score":0.7329999804496765},{"id":"https://openalex.org/keywords/majorana-fermions","display_name":"Majorana fermions","score":0.7649999856948853},{"id":"https://openalex.org/keywords/toric-code","display_name":"toric code","score":0.7739999890327454},{"id":"https://openalex.org/keywords/vortex-excitation","display_name":"vortex excitation","score":0.718999981880188},{"id":"https://openalex.org/keywords/anyons","display_name":"anyons","score":0.7179999947547913},{"id":"https://openalex.org/keywords/dirac-cones","display_name":"Dirac cones","score":0.6589999794960022},{"id":"https://openalex.org/keywords/collinear-magnetic-order","display_name":"collinear magnetic order","score":0.5350000262260437},{"id":"https://openalex.org/keywords/topological-phases","display_name":"topological phases","score":0.6399999856948853},{"id":"https://openalex.org/keywords/projected-entangled-pair-states","display_name":"projected entangled pair states","score":0.7379999756813049},{"id":"https://openalex.org/keywords/linear-spin-wave-theory","display_name":"linear spin-wave theory","score":0.7940000295639038}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6586999893188477},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.640500009059906},{"id":"https://openalex.org/C84883863","wikidata":"https://www.wikidata.org/wiki/Q7825777","display_name":"Toric code","level":4,"score":0.5856000185012817},{"id":"https://openalex.org/C52233224","wikidata":"https://www.wikidata.org/wiki/Q44363","display_name":"Fermion","level":2,"score":0.5644999742507935},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.477400004863739},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.4641000032424927},{"id":"https://openalex.org/C69523127","wikidata":"https://www.wikidata.org/wiki/Q4480008","display_name":"Ground state","level":2,"score":0.4146000146865845},{"id":"https://openalex.org/C140820882","wikidata":"https://www.wikidata.org/wiki/Q732722","display_name":"Vortex","level":2,"score":0.3935000002384186},{"id":"https://openalex.org/C2778761060","wikidata":"https://www.wikidata.org/wiki/Q6714234","display_name":"MAJORANA","level":3,"score":0.3723999857902527},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.3596000075340271},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.35089999437332153},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.3440999984741211},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.33629998564720154},{"id":"https://openalex.org/C201665358","wikidata":"https://www.wikidata.org/wiki/Q899196","display_name":"Heisenberg model","level":3,"score":0.323199987411499},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.32109999656677246},{"id":"https://openalex.org/C174084160","wikidata":"https://www.wikidata.org/wiki/Q908049","display_name":"Bound state","level":2,"score":0.31850001215934753},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.3149000108242035},{"id":"https://openalex.org/C75577371","wikidata":"https://www.wikidata.org/wiki/Q6497124","display_name":"Lattice model (finance)","level":3,"score":0.3100000023841858},{"id":"https://openalex.org/C155355069","wikidata":"https://www.wikidata.org/wiki/Q575224","display_name":"Antiferromagnetism","level":2,"score":0.30880001187324524},{"id":"https://openalex.org/C2983197053","wikidata":"https://www.wikidata.org/wiki/Q654182","display_name":"Energy spectrum","level":2,"score":0.30809998512268066},{"id":"https://openalex.org/C114410712","wikidata":"https://www.wikidata.org/wiki/Q973321","display_name":"Hypersurface","level":2,"score":0.30489999055862427},{"id":"https://openalex.org/C181830111","wikidata":"https://www.wikidata.org/wiki/Q214850","display_name":"Gauge theory","level":2,"score":0.29670000076293945},{"id":"https://openalex.org/C90626534","wikidata":"https://www.wikidata.org/wiki/Q4523381","display_name":"Hexagonal lattice","level":3,"score":0.29649999737739563},{"id":"https://openalex.org/C85906118","wikidata":"https://www.wikidata.org/wiki/Q186693","display_name":"Phase diagram","level":3,"score":0.29350000619888306},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.289000004529953},{"id":"https://openalex.org/C82217956","wikidata":"https://www.wikidata.org/wiki/Q184207","display_name":"Ferromagnetism","level":2,"score":0.2831999957561493},{"id":"https://openalex.org/C79955541","wikidata":"https://www.wikidata.org/wiki/Q1348371","display_name":"Dirac fermion","level":3,"score":0.2775000035762787},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2727999985218048},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.26260000467300415},{"id":"https://openalex.org/C2778351468","wikidata":"https://www.wikidata.org/wiki/Q17149634","display_name":"Matrix product state","level":4,"score":0.2567000091075897},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.2563000023365021},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.2540999948978424}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.33454","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33454","pdf_url":"https://arxiv.org/pdf/2609.33454","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.33454","doi":"https://doi.org/10.48550/arxiv.2609.33454","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.33454","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:2609.33454","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33454","pdf_url":"https://arxiv.org/pdf/2609.33454","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":null,"license_id":null,"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/G1352909968","display_name":null,"funder_award_id":"\u223cSP22231244CPETWOQCDHOC","funder_id":"https://openalex.org/F4320322211","funder_display_name":"Indian Institute of Technology Madras"},{"id":"https://openalex.org/G7002119356","display_name":"Kavli Institute for Theoretical Physics","funder_award_id":"2309135","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320310042","display_name":"Aspen Center for Physics","ror":"https://ror.org/05gqcbq50"},{"id":"https://openalex.org/F4320322211","display_name":"Indian Institute of Technology Madras","ror":"https://ror.org/03v0r5n49"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214804402.pdf","grobid_xml":"https://content.openalex.org/works/W7214804402.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W1570334424","https://openalex.org/W1815618239","https://openalex.org/W7168429952"],"related_works":["https://openalex.org/W2994628662","https://openalex.org/W1965032203","https://openalex.org/W6920133356","https://openalex.org/W7168429952","https://openalex.org/W2913089378","https://openalex.org/W2983086351","https://openalex.org/W2886992638","https://openalex.org/W4385365706","https://openalex.org/W1915776630","https://openalex.org/W3213259200"],"abstract_inverted_index":{"We":[0,18,65,124,207],"study":[1,168],"the":[2,7,15,24,33,41,48,52,72,82,103,119,130,135,151,169,175,184,215],"spin-$1/2$":[3],"Kitaev-Heisenberg":[4,34,153],"model":[5,27,35,54],"on":[6,20,102,107],"square-hexagon-dodecagon":[8],"lattice":[9],"with":[10,28,36],"a":[11,56,61,67,78,87,96,210,219],"symmetry-preserving":[12],"tri-coloring":[13],"of":[14,43,51,134,146,204],"Kitaev":[16,26,38,53,185],"exchanges.":[17],"focus":[19],"two":[21],"cases:":[22],"(i)":[23],"pure":[25],"anisotropic":[29],"exchanges":[30],"and":[31,110,121,138,163,201],"(ii)":[32],"isotropic":[37,152],"exchange.":[39],"In":[40],"absence":[42],"Heisenberg":[44],"interactions,":[45],"we":[46,155,187],"use":[47],"standard":[49],"mapping":[50],"onto":[55],"quadratic":[57],"Majorana-fermion":[58],"problem":[59],"in":[60],"$\\mathbb{Z}_2$":[62],"gauge":[63],"field.":[64],"find":[66],"gapped":[68,92],"energy":[69,84],"spectrum":[70],"throughout":[71],"positive-coupling":[73],"phase":[74,171],"diagram,":[75],"except":[76],"at":[77,213],"single":[79],"point":[80,212],"where":[81],"twofold-degenerate":[83],"bands":[85],"form":[86],"Dirac":[88],"cone.":[89],"This":[90],"unique":[91],"region":[93],"corresponds":[94],"to":[95,118,167],"toric":[97,176],"code":[98,177],"phase.":[99],"However,":[100],"depending":[101],"couplings,":[104],"vortex":[105,136],"excitations":[106],"square,":[108],"hexagonal,":[109],"dodecagonal":[111],"plaquettes":[112],"realize":[113],"three":[114],"distinct":[115],"relative":[116,127,202],"assignments":[117,128],"$e$":[120],"$m$":[122],"anyons.":[123],"determine":[125],"these":[126],"from":[129,174],"physical":[131],"fermion":[132],"parity":[133],"sectors":[137],"locate":[139],"their":[140,199],"boundaries":[141],"by":[142,198],"tracking":[143],"zero":[144],"crossings":[145],"vortex-bound":[147],"Majorana":[148],"levels.":[149],"For":[150],"model,":[154],"combine":[156],"graph-based":[157],"projected":[158],"entangled-pair-state":[159],"calculations,":[160],"exact":[161],"diagonalizations,":[162],"linear":[164],"spin-wave":[165],"theory":[166],"entire":[170],"diagram.":[172],"Apart":[173],"topological":[178],"phases":[179,193],"that":[180,194],"are":[181],"robust":[182],"around":[183],"limits,":[186],"obtain":[188],"four":[189],"collinear":[190],"magnetically":[191],"ordered":[192],"can":[195],"be":[196],"characterized":[197],"local":[200],"orderings":[203],"hexagonal":[205],"plaquettes.":[206],"also":[208],"identify":[209],"special":[211],"which":[214],"ground":[216],"state":[217],"is":[218],"product":[220],"state.":[221]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}