{"id":"https://openalex.org/W1948828652","doi":null,"title":"Towards a Complete Classification of Symmetry-Protected Phases for Interacting Fermions in Two Dimensions","display_name":"Towards a Complete Classification of Symmetry-Protected Phases for Interacting Fermions in Two Dimensions","publication_year":2015,"publication_date":"2015-01-06","ids":{"openalex":"https://openalex.org/W1948828652","mag":"1948828652"},"language":"en","primary_location":{"id":"mag:1948828652","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1501.01313.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"volume":null,"type":"preprint","indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1501.01313.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","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":[],"countries":[],"is_corresponding":false,"raw_author_name":"Meng Cheng","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-7600-1809","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035971150","display_name":"Zhen Bi","orcid":"https://orcid.org/0000-0003-0351-3963","observed_orcids":["https://orcid.org/0000-0003-0351-3963"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhen Bi","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-0351-3963","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015225562","display_name":"Yi\u2010Zhuang You","orcid":"https://orcid.org/0000-0003-4080-5340","observed_orcids":["https://orcid.org/0000-0003-4080-5340"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yi\u2010Zhuang You","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-4080-5340","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5046071106","display_name":"Zheng\u2010Cheng Gu","orcid":"https://orcid.org/0000-0002-7269-6401","observed_orcids":["https://orcid.org/0000-0002-7269-6401"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zheng\u2010Cheng Gu","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-7269-6401","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":18,"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/T10657","display_name":"Topological Materials and Phenomena","score":0.711899995803833,"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/T10657","display_name":"Topological Materials and Phenomena","score":0.711899995803833,"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/T11804","display_name":"Quantum many-body systems","score":0.249099999666214,"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/T11682","display_name":"Advanced Condensed Matter Physics","score":0.01549999974668026,"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/symmetry-protected-topological-phases","display_name":"symmetry-protected topological phases","score":0.996999979019165},{"id":"https://openalex.org/keywords/interacting-fermions","display_name":"interacting fermions","score":0.9860000014305115},{"id":"https://openalex.org/keywords/two-dimensional-systems","display_name":"two-dimensional systems","score":0.7990000247955322},{"id":"https://openalex.org/keywords/time-reversal-symmetry","display_name":"time-reversal symmetry","score":0.9629999995231628},{"id":"https://openalex.org/keywords/group-cohomology","display_name":"group cohomology","score":0.6290000081062317},{"id":"https://openalex.org/keywords/z2-symmetry","display_name":"Z2 symmetry","score":0.34700000286102295}],"concepts":[{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.7335329055786133},{"id":"https://openalex.org/C52233224","wikidata":"https://www.wikidata.org/wiki/Q44363","display_name":"Fermion","level":2,"score":0.6927361488342285},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.6842401027679443},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.6438531875610352},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6265488862991333},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.613094687461853},{"id":"https://openalex.org/C44306375","wikidata":"https://www.wikidata.org/wiki/Q902019","display_name":"Symmetry group","level":2,"score":0.6032799482345581},{"id":"https://openalex.org/C155751095","wikidata":"https://www.wikidata.org/wiki/Q1408937","display_name":"Group cohomology","level":3,"score":0.5701854825019836},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5251290798187256},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4862024188041687},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.4358595609664917},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4136263430118561},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3335787057876587},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.33336925506591797},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.25426334142684937},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2527417540550232},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14799979329109192},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07583445310592651},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.053429245948791504},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:1948828652","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1501.01313.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"mag:1948828652","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1501.01313.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W6910709126","https://openalex.org/W2545306594","https://openalex.org/W1663844468","https://openalex.org/W2171135483","https://openalex.org/W2899175753","https://openalex.org/W2202024260","https://openalex.org/W2973189266","https://openalex.org/W2963727712","https://openalex.org/W1605583690","https://openalex.org/W3205376154"],"abstract_inverted_index":{"Recently,":[0],"it":[1],"has":[2],"been":[3],"shown":[4],"that":[5,76],"two-dimensional":[6,90],"bosonic":[7],"symmetry-protected":[8],"topological(SPT)":[9],"phases":[10,39,88,112],"with":[11,77],"on-site":[12],"unitary":[13,58],"symmetry":[14,97],"$G$":[15],"can":[16,100],"be":[17,101],"completely":[18],"classified":[19],"by":[20,70,114],"the":[21,52,66,106],"group":[22,28,71,98],"cohomology":[23],"class":[24,30],"$H^3(G,":[25],"\\mathrm{U}(1))$.":[26],"Later,":[27],"super-cohomology":[29],"was":[31],"proposed":[32],"as":[33],"a":[34,83,95],"partial":[35,67],"classification":[36,85,107],"for":[37,89,94],"SPT":[38,87,111],"of":[40,55,57,86,108],"interacting":[41,91,109],"fermions.":[42],"In":[43],"this":[44,48],"work,":[45],"we":[46,74],"revisit":[47],"problem":[49],"based":[50],"on":[51],"mathematical":[53],"framework":[54],"$G$-extension":[56],"braided":[59],"tensor":[60],"category(UBTC)":[61],"theory.":[62],"We":[63,103],"first":[64],"reproduce":[65],"classifications":[68],"given":[69],"super-cohomology,":[72],"then":[73],"show":[75],"an":[78],"additional":[79],"$H^1(G,":[80],"\\mathbb{Z}_2)$":[81],"structure,":[82],"complete":[84],"fermion":[92],"systems":[93],"total":[96],"$G\\times\\mathbb{Z}_2^f$":[99],"achieved.":[102],"also":[104],"discuss":[105],"fermionic":[110],"protected":[113],"time-reversal":[115],"symmetry.":[116]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3}],"updated_date":"2026-11-03T10:50:19.383937","created_date":"2016-06-24T00:00:00"}