{"id":"https://openalex.org/W7225189779","doi":"https://doi.org/10.48550/arxiv.2611.03241","title":"Establishing N\u00e9el order in the square-lattice antiferromagnetic Heisenberg model: a bootstrap proof","display_name":"Establishing N\u00e9el order in the square-lattice antiferromagnetic Heisenberg model: a bootstrap proof","publication_year":2026,"publication_date":"2026-11-02","ids":{"openalex":"https://openalex.org/W7225189779","doi":"https://doi.org/10.48550/arxiv.2611.03241"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2611.03241","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2611.03241","pdf_url":"https://arxiv.org/pdf/2611.03241","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2611.03241","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5092449897","display_name":"Nisarg Chadha","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chadha, Nisarg","raw_affiliation_strings":["Department of Physics , Harvard University , Cambridge MA 02138 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics , Harvard University , Cambridge MA 02138 , USA","institution_ids":["https://openalex.org/I136199984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5160472160","display_name":"Taige Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wang, Taige","raw_affiliation_strings":["Department of Physics , Harvard University , Cambridge MA 02138 , USA","Materials Research Laboratory , Massachusetts Institute of Technology , Cambridge , MA 02139 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics , Harvard University , Cambridge MA 02138 , USA","institution_ids":["https://openalex.org/I136199984"]},{"raw_affiliation_string":"Materials Research Laboratory , Massachusetts Institute of Technology , Cambridge , MA 02139 , USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001656369","display_name":"P. A. Nosov","orcid":"https://orcid.org/0000-0002-4829-4939","observed_orcids":["https://orcid.org/0000-0002-4829-4939"]},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nosov, Pavel A.","raw_affiliation_strings":["Department of Physics , Harvard University , Cambridge MA 02138 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics , Harvard University , Cambridge MA 02138 , USA","institution_ids":["https://openalex.org/I136199984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048433050","display_name":"Michael G. Scheer","orcid":"https://orcid.org/0000-0003-0798-6135","observed_orcids":["https://orcid.org/0000-0003-0798-6135"]},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Scheer, Michael G.","raw_affiliation_strings":["Department of Physics , Harvard University , Cambridge MA 02138 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics , Harvard University , Cambridge MA 02138 , USA","institution_ids":["https://openalex.org/I136199984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034171340","display_name":"Eslam Khalaf","orcid":"https://orcid.org/0000-0001-9298-1245","observed_orcids":["https://orcid.org/0000-0001-9298-1245"]},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Khalaf, Eslam","raw_affiliation_strings":["Department of Physics , Harvard University , Cambridge MA 02138 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics , Harvard University , Cambridge MA 02138 , USA","institution_ids":["https://openalex.org/I136199984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"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/T11804","display_name":"Quantum many-body systems","score":0.9336000084877014,"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"}},"topics":[{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":0.9336000084877014,"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":0.028999999165534973,"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/T11682","display_name":"Advanced Condensed Matter Physics","score":0.02290000021457672,"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/antiferromagnetic-order","display_name":"antiferromagnetic ordering","score":0.996999979019165},{"id":"https://openalex.org/keywords/spontaneous-symmetry-breaking","display_name":"spontaneous symmetry breaking","score":0.8519999980926514},{"id":"https://openalex.org/keywords/square-lattice-antiferromagnet","display_name":"square lattice antiferromagnet","score":0.8809999823570251},{"id":"https://openalex.org/keywords/heisenberg-antiferromagnet","display_name":"Heisenberg antiferromagnet","score":0.8199999928474426},{"id":"https://openalex.org/keywords/xxz-model","display_name":"XXZ model","score":0.9739999771118164},{"id":"https://openalex.org/keywords/bootstrap-method","display_name":"bootstrapping","score":0.42800000309944153},{"id":"https://openalex.org/keywords/infrared-bounds","display_name":"infrared bounds","score":0.8119999766349792},{"id":"https://openalex.org/keywords/long-range-order","display_name":"long-range order","score":0.8970000147819519},{"id":"https://openalex.org/keywords/matrix-product-states","display_name":"matrix product states","score":0.8450000286102295},{"id":"https://openalex.org/keywords/thermodynamic-limit","display_name":"thermodynamic limit","score":0.9079999923706055},{"id":"https://openalex.org/keywords/two-dimensional-spin-models","display_name":"two-dimensional spin systems","score":0.6150000095367432}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6398000121116638},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5690000057220459},{"id":"https://openalex.org/C201665358","wikidata":"https://www.wikidata.org/wiki/Q899196","display_name":"Heisenberg model","level":3,"score":0.5338000059127808},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.45719999074935913},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.4521999955177307},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.44859999418258667},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4341000020503998},{"id":"https://openalex.org/C155355069","wikidata":"https://www.wikidata.org/wiki/Q575224","display_name":"Antiferromagnetism","level":2,"score":0.41280001401901245},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.392300009727478},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3732999861240387},{"id":"https://openalex.org/C54021167","wikidata":"https://www.wikidata.org/wiki/Q1103484","display_name":"Thermodynamic limit","level":2,"score":0.35269999504089355},{"id":"https://openalex.org/C2778351468","wikidata":"https://www.wikidata.org/wiki/Q17149634","display_name":"Matrix product state","level":4,"score":0.3303999900817871},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.3246000111103058},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.3181000053882599},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.31200000643730164},{"id":"https://openalex.org/C201640847","wikidata":"https://www.wikidata.org/wiki/Q2362924","display_name":"Complete lattice","level":3,"score":0.30250000953674316},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.29589998722076416},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.28349998593330383},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.2824999988079071},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.2802000045776367},{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.2754000127315521},{"id":"https://openalex.org/C119350121","wikidata":"https://www.wikidata.org/wiki/Q1091134","display_name":"Commensurability (mathematics)","level":2,"score":0.275299996137619},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27489998936653137},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.2732999920845032},{"id":"https://openalex.org/C174084160","wikidata":"https://www.wikidata.org/wiki/Q908049","display_name":"Bound state","level":2,"score":0.2709999978542328},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2671000063419342},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.26489999890327454},{"id":"https://openalex.org/C56911000","wikidata":"https://www.wikidata.org/wiki/Q831774","display_name":"Density matrix","level":3,"score":0.26330000162124634},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.262800008058548},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.2621999979019165},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.25949999690055847},{"id":"https://openalex.org/C202854965","wikidata":"https://www.wikidata.org/wiki/Q3044470","display_name":"Constructive proof","level":2,"score":0.2500999867916107}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2611.03241","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2611.03241","pdf_url":"https://arxiv.org/pdf/2611.03241","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.2611.03241","doi":"https://doi.org/10.48550/arxiv.2611.03241","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2611.03241","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:2611.03241","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2611.03241","pdf_url":"https://arxiv.org/pdf/2611.03241","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":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320306202","display_name":"Gordon and Betty Moore Foundation","ror":"https://ror.org/006wxqw41"},{"id":"https://openalex.org/F4320309036","display_name":"Purdue University","ror":"https://ror.org/02dqehb95"},{"id":"https://openalex.org/F4320309622","display_name":"Harvard University","ror":"https://ror.org/03vek6s52"},{"id":"https://openalex.org/F4320314484","display_name":"Julian Schwinger Foundation for Physics Research","ror":"https://ror.org/01862bd29"},{"id":"https://openalex.org/F4320337367","display_name":"Division of Materials Research","ror":"https://ror.org/01pc7k308"},{"id":"https://openalex.org/F4320337377","display_name":"Office of Advanced Cyberinfrastructure","ror":"https://ror.org/04nh1dc89"},{"id":"https://openalex.org/F4320338027","display_name":"FAS Division of Science, Harvard University","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7225189779.pdf","grobid_xml":"https://content.openalex.org/works/W7225189779.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1991991544","https://openalex.org/W2147375813","https://openalex.org/W1970670359","https://openalex.org/W1755100590","https://openalex.org/W1995450100","https://openalex.org/W4416778203","https://openalex.org/W2035072876","https://openalex.org/W2090874270","https://openalex.org/W2083078684","https://openalex.org/W2048834806"],"abstract_inverted_index":{"Rigorously":[0],"establishing":[1],"spontaneous":[2],"symmetry":[3],"breaking":[4],"(SSB)":[5],"in":[6,67,98,155,173],"the":[7,17,27,62,68,83,94,99,103,115,125,150,170,174],"thermodynamic":[8,175],"limit":[9,176],"is":[10,14,32,158],"generally":[11],"challenging.":[12],"This":[13],"exemplified":[15],"by":[16,75],"two-dimensional":[18],"(2D)":[19],"$S":[20,70],"=":[21,71],"1/2$":[22,72],"antiferromagnetic":[23],"Heisenberg":[24],"model":[25,74],"where":[26],"existence":[28,63,126],"of":[29,42,64,90,93,114,127],"N\u00e9el":[30,65,84],"order":[31,66,85,129],"not":[33],"rigorously":[34,54],"established":[35],"despite":[36],"overwhelming":[37],"evidence":[38],"from":[39,177],"a":[40,47,77,88,112,159],"variety":[41],"methods.":[43],"We":[44,136],"show":[45],"that":[46],"bootstrap":[48],"approach":[49,110,182],"can":[50,183,197],"be":[51,184,198],"used":[52],"to":[53,60,123,130,187],"establish":[55],"SSB":[56],"and":[57],"use":[58,119],"it":[59],"prove":[61],"2D":[69],"XXZ":[73],"deriving":[76],"strictly":[78],"positive":[79],"lower":[80],"bound":[81,122],"on":[82,132,169],"parameter":[86,96],"for":[87,140,162,192],"set":[89],"discrete":[91],"values":[92],"anisotropy":[95],"$\u0394$":[97],"range":[100],"$[0,2]$":[101],"including":[102],"isotropic":[104],"(Heisenberg)":[105],"point":[106],"$\u0394=":[107],"1$.":[108],"Our":[109,181],"employs":[111],"generalization":[113],"Kennedy--Lieb--Shastry":[116],"inequalities,":[117],"which":[118,193],"an":[120],"infrared":[121,194],"reduce":[124],"long-range":[128],"bounds":[131,139,168,196],"certain":[133],"finite-distance":[134],"correlators.":[135],"compute":[137],"these":[138],"all":[141],"sufficiently":[142],"large":[143],"systems":[144],"with":[145],"periodic":[146],"boundary":[147],"conditions":[148],"using":[149],"bootstrap.":[151],"An":[152],"important":[153],"ingredient":[154],"our":[156],"proof":[157],"novel":[160],"method":[161],"obtaining":[163],"exactly":[164],"certified":[165],"variational":[166],"upper":[167],"energy":[171],"density":[172],"matrix":[178],"product":[179],"states.":[180],"readily":[185],"generalized":[186],"other":[188],"local":[189],"lattice":[190],"models":[191],"susceptibility":[195],"obtained.":[199]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-11-04T00:00:00"}