{"id":"https://openalex.org/W3103909720","doi":null,"title":"Partition Functions and Stability Criteria of Topological Insulators","display_name":"Partition Functions and Stability Criteria of Topological Insulators","publication_year":2016,"publication_date":"2016-08-16","ids":{"openalex":"https://openalex.org/W3103909720","mag":"3103909720"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.753.8216","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.753.8216","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1309.2155.pdf","raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078015556","display_name":"Andrea Cappelli A","orcid":"https://orcid.org/0000-0003-1306-4698","observed_orcids":["https://orcid.org/0000-0003-1306-4698"]},"institutions":[{"id":"https://openalex.org/I4210133295","display_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Firenze","ror":"https://ror.org/02vv5y108","country_code":"IT","type":"facility","lineage":["https://openalex.org/I160013858","https://openalex.org/I4210133295"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Andrea Cappelli","raw_affiliation_strings":["INFN, Via G. Sansone 1, 50019, Sesto Fiorentino, Firenze, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INFN, Via G. Sansone 1, 50019, Sesto Fiorentino, Firenze, Italy","institution_ids":["https://openalex.org/I4210133295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056263443","display_name":"Enrico Randellini","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Enrico Randellini","raw_affiliation_strings":["Dipartimento di Fisica, Universit\u00e0 di Firenze, Via G. Sansone 1, 50019, Sesto Fiorentino, Firenze, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Fisica, Universit\u00e0 di Firenze, Via G. Sansone 1, 50019, Sesto Fiorentino, Firenze, Italy","institution_ids":["https://openalex.org/I45084792"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5078015556"],"corresponding_institution_ids":["https://openalex.org/I4210133295"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":23,"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":0.9990000128746033,"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/T10657","display_name":"Topological Materials and Phenomena","score":0.9990000128746033,"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":0.0003000000142492354,"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":0.00019999999494757503,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/topological-insulators","display_name":"topological insulators","score":0.9869999885559082},{"id":"https://openalex.org/keywords/quantum-spin-hall-effect","display_name":"quantum spin Hall effect","score":0.8629999756813049},{"id":"https://openalex.org/keywords/partition-function","display_name":"partition function","score":0.8199999928474426},{"id":"https://openalex.org/keywords/time-reversal-symmetry","display_name":"time-reversal symmetry","score":0.8080000281333923},{"id":"https://openalex.org/keywords/topological-phase-stability","display_name":"topological phase stability","score":0.8379999995231628},{"id":"https://openalex.org/keywords/modular-invariance","display_name":"modular invariance","score":0.9769999980926514},{"id":"https://openalex.org/keywords/z2-topological-invariant","display_name":"Z2 topological invariant","score":0.8650000095367432}],"concepts":[{"id":"https://openalex.org/C45646460","wikidata":"https://www.wikidata.org/wiki/Q17165159","display_name":"Topological order","level":3,"score":0.7480407357215881},{"id":"https://openalex.org/C2778401447","wikidata":"https://www.wikidata.org/wiki/Q7140637","display_name":"Partition function (quantum field theory)","level":2,"score":0.707756757736206},{"id":"https://openalex.org/C128911142","wikidata":"https://www.wikidata.org/wiki/Q1488689","display_name":"Topological insulator","level":2,"score":0.7028223276138306},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.5685629844665527},{"id":"https://openalex.org/C92542899","wikidata":"https://www.wikidata.org/wiki/Q7661340","display_name":"Symmetry protected topological order","level":4,"score":0.5133882761001587},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.496634304523468},{"id":"https://openalex.org/C200369452","wikidata":"https://www.wikidata.org/wiki/Q1047822","display_name":"Quantum Hall effect","level":3,"score":0.4865188002586365},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.4614397883415222},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4499616324901581},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.44907692074775696},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4131758511066437},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.35694167017936707},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.32397595047950745},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2616581916809082},{"id":"https://openalex.org/C147120987","wikidata":"https://www.wikidata.org/wiki/Q2225","display_name":"Electron","level":2,"score":0.15045595169067383},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.10847872495651245},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.753.8216","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.753.8216","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1309.2155.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":61,"referenced_works":["https://openalex.org/W47131799","https://openalex.org/W1451104134","https://openalex.org/W1489060875","https://openalex.org/W1520371613","https://openalex.org/W1520510487","https://openalex.org/W1541963827","https://openalex.org/W1552055731","https://openalex.org/W1601700513","https://openalex.org/W1605377265","https://openalex.org/W1620821418","https://openalex.org/W1816380889","https://openalex.org/W1816505947","https://openalex.org/W1905539406","https://openalex.org/W1967475705","https://openalex.org/W1969128440","https://openalex.org/W1971531461","https://openalex.org/W1971925129","https://openalex.org/W1974065616","https://openalex.org/W1974674403","https://openalex.org/W1983970619","https://openalex.org/W1984334615","https://openalex.org/W1990963622","https://openalex.org/W1991616904","https://openalex.org/W2003397144","https://openalex.org/W2007715780","https://openalex.org/W2008188057","https://openalex.org/W2010759393","https://openalex.org/W2020332193","https://openalex.org/W2020748173","https://openalex.org/W2021857174","https://openalex.org/W2022144970","https://openalex.org/W2024100012","https://openalex.org/W2031028572","https://openalex.org/W2031749334","https://openalex.org/W2043175787","https://openalex.org/W2047283298","https://openalex.org/W2047786902","https://openalex.org/W2054741213","https://openalex.org/W2064989124","https://openalex.org/W2071525227","https://openalex.org/W2075485937","https://openalex.org/W2083123179","https://openalex.org/W2088198211","https://openalex.org/W2090004722","https://openalex.org/W2104740527","https://openalex.org/W2111640030","https://openalex.org/W2120831645","https://openalex.org/W2128019891","https://openalex.org/W2128459818","https://openalex.org/W2129159306","https://openalex.org/W2159478153","https://openalex.org/W2164792320","https://openalex.org/W2166606564","https://openalex.org/W2196824302","https://openalex.org/W2334243442","https://openalex.org/W2577281216","https://openalex.org/W3105580238","https://openalex.org/W3121974050","https://openalex.org/W3141849522","https://openalex.org/W4206688401","https://openalex.org/W4301787874"],"related_works":["https://openalex.org/W3101389886","https://openalex.org/W1998055169","https://openalex.org/W2047283298","https://openalex.org/W3195219641","https://openalex.org/W2026928919","https://openalex.org/W7204669220","https://openalex.org/W2153302397","https://openalex.org/W2035188708","https://openalex.org/W3010909467","https://openalex.org/W1967475705"],"abstract_inverted_index":{"The":[0,20,54],"non-chiral":[1],"edge":[2,69],"excitations":[3],"of":[4,16,22,41,47,50,57],"quantum":[5],"spin":[6],"Hall":[7],"systems":[8,64],"and":[9,34,44,67],"topological":[10,23,59],"insu-lators":[11],"are":[12],"described":[13],"by":[14,26],"means":[15],"their":[17],"partition":[18,52],"function.":[19,53],"stability":[21],"phases":[24],"protected":[25],"time-reversal":[27],"symmetry":[28],"is":[29,61],"rediscussed":[30],"in":[31,36],"this":[32],"context":[33],"put":[35],"relation":[37],"with":[38,65],"the":[39,45,51],"existence":[40],"discrete":[42],"anomalies":[43],"lack":[46],"modular":[48],"invariance":[49],"Z2":[55],"characterization":[56],"stable":[58],"insulators":[60],"extended":[62],"to":[63],"interacting":[66],"non-Abelian":[68],"excitations.":[70],"ar":[71],"X":[72],"iv":[73]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":5}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2020-11-23T00:00:00"}