{"id":"https://openalex.org/W2020293442","doi":"https://doi.org/10.1103/physrevb.78.125104","title":"Band touching from real-space topology in frustrated hopping models","display_name":"Band touching from real-space topology in frustrated hopping models","publication_year":2008,"publication_date":"2008-09-10","ids":{"openalex":"https://openalex.org/W2020293442","doi":"https://doi.org/10.1103/physrevb.78.125104","mag":"2020293442"},"language":"en","primary_location":{"id":"doi:10.1103/physrevb.78.125104","doi":"https://doi.org/10.1103/physrevb.78.125104","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrevb.78.125104","pdf_url":null,"source":{"id":"https://openalex.org/S6791298","display_name":"Physical Review B","issn_l":"1098-0121","issn":["1098-0121","1538-4489","1550-235X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","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"},"parent_works":[],"lineage":["https://openalex.org/W2020293442"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0803.3628","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035939119","display_name":"Doron L. Bergman","orcid":null,"observed_orcids":[]},"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":"Doron L. Bergman","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":"middle","author":{"id":"https://openalex.org/A5077222936","display_name":"Congjun Wu","orcid":"https://orcid.org/0000-0001-5191-6869","observed_orcids":["https://orcid.org/0000-0001-5191-6869","https://orcid.org/0000-0001-5240-6852"]},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Congjun Wu","raw_affiliation_strings":["Department of Physics, University of California, San Diego, La Jolla, California 92093-0319, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, University of California, San Diego, La Jolla, California 92093-0319, USA","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014003147","display_name":"Leon Balents","orcid":"https://orcid.org/0000-0002-2377-2711","observed_orcids":["https://orcid.org/0000-0002-2377-2711"]},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]},{"id":"https://openalex.org/I4405259940","display_name":"Kavli Institute for Theoretical Physics","ror":"https://ror.org/02yt0vw44","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I154570441","https://openalex.org/I4405259940"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Leon Balents","raw_affiliation_strings":["Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030, USA","institution_ids":["https://openalex.org/I154570441","https://openalex.org/I4405259940"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2675,"currency":"USD","value_usd":2675},"apc_paid":null,"fwci":4.2903,"has_fulltext":true,"cited_by_count":386,"citation_normalized_percentile":{"value":0.95053885,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"78","issue":"12","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":0.9477999806404114,"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":0.9477999806404114,"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":0.03669999912381172,"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":0.0031999999191612005,"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/flat-bands","display_name":"flat bands","score":0.9729999899864197},{"id":"https://openalex.org/keywords/band-touching","display_name":"band touching","score":0.9559999704360962},{"id":"https://openalex.org/keywords/real-space-topology","display_name":"real-space topology","score":0.9779999852180481},{"id":"https://openalex.org/keywords/topological-protection","display_name":"topological protection","score":0.5899999737739563},{"id":"https://openalex.org/keywords/localized-states","display_name":"localized states","score":0.5329999923706055},{"id":"https://openalex.org/keywords/counting-arguments","display_name":"counting arguments","score":0.765999972820282},{"id":"https://openalex.org/keywords/degeneracy-splitting","display_name":"degeneracy splitting","score":0.7540000081062317},{"id":"https://openalex.org/keywords/periodic-boundary-conditions","display_name":"periodic boundary conditions","score":0.5440000295639038}],"concepts":[{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.676343560218811},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5928714871406555},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5847964286804199},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5498745441436768},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5241637229919434},{"id":"https://openalex.org/C152991086","wikidata":"https://www.wikidata.org/wiki/Q1225362","display_name":"Position and momentum space","level":2,"score":0.5129175186157227},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4422718584537506},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30377358198165894},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2692531943321228},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23991429805755615},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10298272967338562},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.06903818249702454},{"id":"https://openalex.org/C60644358","wikidata":"https://www.wikidata.org/wiki/Q128570","display_name":"Bioinformatics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1103/physrevb.78.125104","doi":"https://doi.org/10.1103/physrevb.78.125104","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrevb.78.125104","pdf_url":null,"source":{"id":"https://openalex.org/S6791298","display_name":"Physical Review B","issn_l":"1098-0121","issn":["1098-0121","1538-4489","1550-235X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","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:0803.3628","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0803.3628","pdf_url":"https://arxiv.org/pdf/0803.3628","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.0803.3628","doi":"https://doi.org/10.48550/arxiv.0803.3628","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.0803.3628","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:0803.3628","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0803.3628","pdf_url":"https://arxiv.org/pdf/0803.3628","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"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2020293442.pdf","grobid_xml":"https://content.openalex.org/works/W2020293442.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1963759189","https://openalex.org/W1966808325","https://openalex.org/W1982408041","https://openalex.org/W1990565252","https://openalex.org/W2003107311","https://openalex.org/W2011570762","https://openalex.org/W2014935324","https://openalex.org/W2029100014","https://openalex.org/W2032527773","https://openalex.org/W2034398864","https://openalex.org/W2038120878","https://openalex.org/W2038531793","https://openalex.org/W2074565952","https://openalex.org/W2085578944","https://openalex.org/W2090010159","https://openalex.org/W2104940755","https://openalex.org/W2129603153","https://openalex.org/W2140200138","https://openalex.org/W2148462133"],"related_works":["https://openalex.org/W4281551440","https://openalex.org/W58439957","https://openalex.org/W3004088210","https://openalex.org/W2009911686","https://openalex.org/W1453926","https://openalex.org/W4414467703","https://openalex.org/W2243776337","https://openalex.org/W7207705284","https://openalex.org/W3176360235","https://openalex.org/W4362585964"],"abstract_inverted_index":{"We":[0,70],"study":[1],"``frustrated''":[2],"hopping":[3],"models,":[4],"in":[5,29,45,67,84,111,121,141],"which":[6,32,80,94,152],"at":[7,61],"least":[8],"one":[9],"energy":[10],"band---at":[11],"the":[12,17,23,43,46,50,58,97,125,134,138,142,155,158],"maximum":[13],"or":[14,119],"minimum":[15],"of":[16,22,42,52,64,127,157],"spectrum---is":[18],"dispersionless.":[19],"The":[20],"states":[21,79,88],"flat":[24,59,159],"band(s)":[25,60],"can":[26,146],"be":[27,148],"represented":[28],"a":[30,39,54,62],"basis,":[31],"is":[33,76,107,116],"fully":[34],"localized,":[35],"having":[36],"support":[37,90],"on":[38,91],"vanishing":[40],"fraction":[41],"system":[44,99],"thermodynamic":[47],"limit.":[48],"In":[49],"majority":[51],"examples,":[53],"dispersive":[55],"band":[56,74,117,139],"touches":[57],"number":[63],"discrete":[65],"points":[66],"momentum":[68],"space.":[69],"demonstrate":[71],"that":[72,109,144],"this":[73],"touching":[75,118],"related":[77],"to":[78,124],"exhibit":[81],"nontrivial":[82],"topology":[83],"real-space.":[85],"Specifically,":[86],"these":[87],"have":[89],"one-dimensional":[92],"loops":[93],"wind":[95],"around":[96],"entire":[98],"(with":[100],"periodic":[101],"boundary":[102],"conditions).":[103],"A":[104],"counting":[105],"argument":[106],"given":[108],"determines,":[110],"each":[112],"case,":[113],"whether":[114],"there":[115],"none,":[120],"precise":[122],"correspondence":[123],"result":[126],"straightforward":[128],"diagonalization.":[129],"When":[130],"they":[131,145],"are":[132],"present,":[133],"topological":[135],"structure":[136],"protects":[137],"touchings":[140],"sense":[143],"only":[147],"removed":[149],"by":[150],"perturbations,":[151],"also":[153],"split":[154],"degeneracy":[156],"band.":[160]},"counts_by_year":[{"year":2026,"cited_by_count":40},{"year":2025,"cited_by_count":53},{"year":2024,"cited_by_count":35},{"year":2023,"cited_by_count":41},{"year":2022,"cited_by_count":25},{"year":2021,"cited_by_count":38},{"year":2020,"cited_by_count":31},{"year":2019,"cited_by_count":19},{"year":2018,"cited_by_count":18},{"year":2017,"cited_by_count":14},{"year":2016,"cited_by_count":16},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":7}],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2016-06-24T00:00:00"}
