{"id":"https://openalex.org/W2969396339","doi":"https://doi.org/10.1103/physrevb.100.155137","title":"Sorting topological stabilizer models in three dimensions","display_name":"Sorting topological stabilizer models in three dimensions","publication_year":2019,"publication_date":"2019-10-23","ids":{"openalex":"https://openalex.org/W2969396339","doi":"https://doi.org/10.1103/physrevb.100.155137","mag":"2969396339"},"language":"en","primary_location":{"id":"doi:10.1103/physrevb.100.155137","doi":"https://doi.org/10.1103/physrevb.100.155137","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrevb.100.155137","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/1908.08049","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059793903","display_name":"Arpit Dua","orcid":"https://orcid.org/0000-0001-6348-4135","observed_orcids":["https://orcid.org/0000-0001-6348-4135"]},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Arpit Dua","raw_affiliation_strings":["Department of Physics, Yale University, New Haven, Connecticut 06520-8120, USA","Yale Quantum Institute, Yale University, New Haven, Connecticut 06520, USA"],"raw_orcid":"https://orcid.org/0000-0001-6348-4135","affiliations":[{"raw_affiliation_string":"Department of Physics, Yale University, New Haven, Connecticut 06520-8120, USA","institution_ids":["https://openalex.org/I32971472"]},{"raw_affiliation_string":"Yale Quantum Institute, Yale University, New Haven, Connecticut 06520, USA","institution_ids":["https://openalex.org/I32971472"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005803611","display_name":"Isaac H. Kim","orcid":"https://orcid.org/0000-0001-7689-3157","observed_orcids":["https://orcid.org/0000-0001-7689-3157"]},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Isaac H. Kim","raw_affiliation_strings":["Stanford Institute for Theoretical Physics, Stanford University, Stanford, California 94305, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Stanford Institute for Theoretical Physics, Stanford University, Stanford, California 94305, USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034971718","display_name":"Meng Cheng","orcid":"https://orcid.org/0000-0001-7600-1809","observed_orcids":["https://orcid.org/0000-0001-7600-1809"]},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Meng Cheng","raw_affiliation_strings":["Department of Physics, Yale University, New Haven, Connecticut 06520-8120, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Yale University, New Haven, Connecticut 06520-8120, USA","institution_ids":["https://openalex.org/I32971472"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060768978","display_name":"Dominic J. Williamson","orcid":"https://orcid.org/0000-0002-8029-6408","observed_orcids":["https://orcid.org/0000-0002-8029-6408"]},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dominic J. Williamson","raw_affiliation_strings":["Department of Physics, Yale University, New Haven, Connecticut 06520-8120, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Yale University, New Haven, Connecticut 06520-8120, USA","institution_ids":["https://openalex.org/I32971472"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.743,"has_fulltext":true,"cited_by_count":53,"citation_normalized_percentile":{"value":0.91510084,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":99},"biblio":{"volume":"100","issue":"15","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":0.8062000274658203,"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":0.8062000274658203,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.05739999935030937,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10657","display_name":"Topological Materials and Phenomena","score":0.04170000180602074,"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/three-dimensional-topological-phases","display_name":"three-dimensional topological phases","score":0.7149999737739563},{"id":"https://openalex.org/keywords/topological-quantum-field-theory","display_name":"topological field theory","score":0.7760000228881836},{"id":"https://openalex.org/keywords/string-operators","display_name":"string operators","score":0.6389999985694885},{"id":"https://openalex.org/keywords/toric-code","display_name":"toric code","score":0.6690000295639038},{"id":"https://openalex.org/keywords/phase-classification","display_name":"phase classification","score":0.5400000214576721}],"concepts":[{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6692489385604858},{"id":"https://openalex.org/C7503960","wikidata":"https://www.wikidata.org/wiki/Q721094","display_name":"Topological quantum field theory","level":2,"score":0.6199555993080139},{"id":"https://openalex.org/C84883863","wikidata":"https://www.wikidata.org/wiki/Q7825777","display_name":"Toric code","level":4,"score":0.559444010257721},{"id":"https://openalex.org/C527218924","wikidata":"https://www.wikidata.org/wiki/Q964053","display_name":"Topological algebra","level":3,"score":0.5491459965705872},{"id":"https://openalex.org/C45646460","wikidata":"https://www.wikidata.org/wiki/Q17165159","display_name":"Topological order","level":3,"score":0.5337563157081604},{"id":"https://openalex.org/C148908050","wikidata":"https://www.wikidata.org/wiki/Q11681505","display_name":"Topological entropy in physics","level":3,"score":0.5270790457725525},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.5134747624397278},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5014839172363281},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4647810459136963},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.45525655150413513},{"id":"https://openalex.org/C2779830401","wikidata":"https://www.wikidata.org/wiki/Q537062","display_name":"Fracton","level":3,"score":0.4525527060031891},{"id":"https://openalex.org/C88548561","wikidata":"https://www.wikidata.org/wiki/Q347599","display_name":"sort","level":2,"score":0.42285069823265076},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4208087921142578},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.41142377257347107},{"id":"https://openalex.org/C77223115","wikidata":"https://www.wikidata.org/wiki/Q634781","display_name":"Topological quantum number","level":2,"score":0.3848778307437897},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.3704862594604492},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.3531414568424225},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.23266035318374634},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.19529998302459717},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.16644427180290222},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14183571934700012},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1358979344367981},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1103/physrevb.100.155137","doi":"https://doi.org/10.1103/physrevb.100.155137","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrevb.100.155137","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:1908.08049","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1908.08049","pdf_url":"https://arxiv.org/pdf/1908.08049","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.1908.08049","doi":"https://doi.org/10.48550/arxiv.1908.08049","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1908.08049","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1908.08049","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1908.08049","pdf_url":"https://arxiv.org/pdf/1908.08049","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/G1070737487","display_name":"CAREER: Interplay of Symmetry and Topology in Condensed Matter Systems","funder_award_id":"1846109","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6354885927","display_name":null,"funder_award_id":"1846109","funder_id":"https://openalex.org/F4320337367","funder_display_name":"Division of Materials Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306151","display_name":"Alfred P. Sloan Foundation","ror":"https://ror.org/052csg198"},{"id":"https://openalex.org/F4320308380","display_name":"Yale University","ror":"https://ror.org/03v76x132"},{"id":"https://openalex.org/F4320337367","display_name":"Division of Materials Research","ror":"https://ror.org/01pc7k308"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2969396339.pdf","grobid_xml":"https://content.openalex.org/works/W2969396339.grobid-xml"},"referenced_works_count":78,"referenced_works":["https://openalex.org/W1537483865","https://openalex.org/W1574355293","https://openalex.org/W1710401991","https://openalex.org/W1740640945","https://openalex.org/W1772750520","https://openalex.org/W1819907849","https://openalex.org/W1970192247","https://openalex.org/W1981304125","https://openalex.org/W1988664331","https://openalex.org/W1992223563","https://openalex.org/W1998186366","https://openalex.org/W2034225373","https://openalex.org/W2035286449","https://openalex.org/W2036559649","https://openalex.org/W2040103735","https://openalex.org/W2050698597","https://openalex.org/W2061320730","https://openalex.org/W2077478049","https://openalex.org/W2090466200","https://openalex.org/W2092686180","https://openalex.org/W2097361916","https://openalex.org/W2114207424","https://openalex.org/W2131690084","https://openalex.org/W2135273380","https://openalex.org/W2141708961","https://openalex.org/W2292979765","https://openalex.org/W2296895255","https://openalex.org/W2298547144","https://openalex.org/W2467626191","https://openalex.org/W2567789734","https://openalex.org/W2571871743","https://openalex.org/W2585753295","https://openalex.org/W2599203539","https://openalex.org/W2606797893","https://openalex.org/W2620136151","https://openalex.org/W2734706981","https://openalex.org/W2747292959","https://openalex.org/W2756856787","https://openalex.org/W2761379279","https://openalex.org/W2763922164","https://openalex.org/W2764174999","https://openalex.org/W2773295121","https://openalex.org/W2775751147","https://openalex.org/W2781070109","https://openalex.org/W2785080930","https://openalex.org/W2792098866","https://openalex.org/W2794912208","https://openalex.org/W2796016079","https://openalex.org/W2804632387","https://openalex.org/W2807786146","https://openalex.org/W2887229962","https://openalex.org/W2889007088","https://openalex.org/W2892972447","https://openalex.org/W2893525927","https://openalex.org/W2894516718","https://openalex.org/W2903211734","https://openalex.org/W2903563595","https://openalex.org/W2904185103","https://openalex.org/W2907998648","https://openalex.org/W2913419161","https://openalex.org/W2914995718","https://openalex.org/W2924199494","https://openalex.org/W2924428627","https://openalex.org/W2932943055","https://openalex.org/W2933625906","https://openalex.org/W2941711605","https://openalex.org/W2945389407","https://openalex.org/W2946793696","https://openalex.org/W2951252175","https://openalex.org/W2956297211","https://openalex.org/W2962768858","https://openalex.org/W2963083281","https://openalex.org/W2965000219","https://openalex.org/W2968123901","https://openalex.org/W2990451371","https://openalex.org/W3011034841","https://openalex.org/W3100008668","https://openalex.org/W6910557939"],"related_works":["https://openalex.org/W3017085904","https://openalex.org/W4404041506","https://openalex.org/W4415262845","https://openalex.org/W2757017840","https://openalex.org/W4249178138","https://openalex.org/W2050698597","https://openalex.org/W1489711308","https://openalex.org/W2781070109","https://openalex.org/W3191295059","https://openalex.org/W2895092930"],"abstract_inverted_index":{"The":[0],"$S$-matrix":[1,63],"invariant":[2,10,41,64],"is":[3,37],"known":[4],"to":[5,24,46,69],"be":[6,67],"complete":[7],"for":[8],"translation":[9,40],"topological":[11,42,51,73,82],"stabilizer":[12,43,74],"models":[13,20,44,75,90,97],"in":[14],"two":[15],"spatial":[16],"dimensions,":[17,34],"as":[18],"such":[19],"are":[21],"phase":[22],"equivalent":[23],"some":[25],"number":[26],"of":[27,29,49,80],"copies":[28],"toric":[30],"code.":[31],"In":[32],"three":[33],"much":[35],"less":[36],"understood":[38],"about":[39],"due":[45],"the":[47,61],"existence":[48],"fracton":[50],"order.":[52],"Here":[53],"we":[54],"introduce":[55],"bulk":[56],"commutation":[57],"quantities":[58],"inspired":[59],"by":[60],"2D":[62],"that":[65],"can":[66],"employed":[68],"coarsely":[70],"sort":[71],"3D":[72],"into":[76],"qualitatively":[77],"distinct":[78],"types":[79],"phases:":[81],"quantum":[83],"field":[84],"theories,":[85],"foliated":[86],"or":[87,95],"fractal":[88],"type-I":[89],"with":[91,98],"rigid":[92],"string":[93,100],"operators,":[94],"type-II":[96],"no":[99],"operators.":[101]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":9},{"year":2018,"cited_by_count":1}],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2019-08-29T00:00:00"}