{"id":"https://openalex.org/W7212010880","doi":"https://doi.org/10.48550/arxiv.2609.07775","title":"Simple invariants for band topology","display_name":"Simple invariants for band topology","publication_year":2026,"publication_date":"2026-09-07","ids":{"openalex":"https://openalex.org/W7212010880","doi":"https://doi.org/10.48550/arxiv.2609.07775"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.07775","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.07775","pdf_url":"https://arxiv.org/pdf/2609.07775","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","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.07775","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020095440","display_name":"Adam Yanis Chaou","orcid":"https://orcid.org/0000-0002-9926-4633","observed_orcids":["https://orcid.org/0000-0002-9926-4633"]},"institutions":[{"id":"https://openalex.org/I47686490","display_name":"Donostia International Physics Center","ror":"https://ror.org/02e24yw40","country_code":"ES","type":"other","lineage":["https://openalex.org/I47686490"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Chaou, Adam Yanis","raw_affiliation_strings":["Donostia International Physics Center , P. Manuel de Lardizabal 4 , 20018 Donostia-San Sebastian , Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Donostia International Physics Center , P. Manuel de Lardizabal 4 , 20018 Donostia-San Sebastian , Spain","institution_ids":["https://openalex.org/I47686490"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005726619","display_name":"Adolfo G. Grushin","orcid":"https://orcid.org/0000-0001-7678-7100","observed_orcids":["https://orcid.org/0000-0001-7678-7100"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Grushin, Adolfo G.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5042877451","display_name":"Peru d\u2019Ornellas","orcid":"https://orcid.org/0000-0002-2349-0044","observed_orcids":["https://orcid.org/0000-0002-2349-0044"]},"institutions":[{"id":"https://openalex.org/I47686490","display_name":"Donostia International Physics Center","ror":"https://ror.org/02e24yw40","country_code":"ES","type":"other","lineage":["https://openalex.org/I47686490"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"d'Ornellas, Peru","raw_affiliation_strings":["Donostia International Physics Center , P. Manuel de Lardizabal 4 , 20018 Donostia-San Sebastian , Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Donostia International Physics Center , P. Manuel de Lardizabal 4 , 20018 Donostia-San Sebastian , Spain","institution_ids":["https://openalex.org/I47686490"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"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/T10657","display_name":"Topological Materials and Phenomena","score":1.0,"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":1.0,"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/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.0,"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":0.0,"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/topological-invariants","display_name":"topological invariants","score":0.902999997138977},{"id":"https://openalex.org/keywords/band-topology","display_name":"band topology","score":0.984000027179718},{"id":"https://openalex.org/keywords/spectral-localizer","display_name":"spectral localizer","score":0.8989999890327454},{"id":"https://openalex.org/keywords/pfaffian","display_name":"Pfaffian","score":0.7160000205039978},{"id":"https://openalex.org/keywords/atomic-limit","display_name":"atomic limit","score":0.6600000262260437}],"concepts":[{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.6894999742507935},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.670199990272522},{"id":"https://openalex.org/C2775956649","wikidata":"https://www.wikidata.org/wiki/Q1189744","display_name":"Pfaffian","level":2,"score":0.5008000135421753},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48989999294281006},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.4262999892234802},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4189000129699707},{"id":"https://openalex.org/C180987920","wikidata":"https://www.wikidata.org/wiki/Q922339","display_name":"Topological ring","level":4,"score":0.4077000021934509},{"id":"https://openalex.org/C77223115","wikidata":"https://www.wikidata.org/wiki/Q634781","display_name":"Topological quantum number","level":2,"score":0.3598000109195709},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.31349998712539673},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3068000078201294},{"id":"https://openalex.org/C171268870","wikidata":"https://www.wikidata.org/wiki/Q1486676","display_name":"GRASP","level":2,"score":0.2944999933242798},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28380000591278076},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.2818000018596649},{"id":"https://openalex.org/C148908050","wikidata":"https://www.wikidata.org/wiki/Q11681505","display_name":"Topological entropy in physics","level":3,"score":0.2808000147342682},{"id":"https://openalex.org/C181576044","wikidata":"https://www.wikidata.org/wiki/Q4129926","display_name":"Computational topology","level":3,"score":0.2705000042915344},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C129089157","wikidata":"https://www.wikidata.org/wiki/Q621550","display_name":"General topology","level":3,"score":0.25600001215934753},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2535000145435333},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.25209999084472656},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.251800000667572}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.07775","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.07775","pdf_url":"https://arxiv.org/pdf/2609.07775","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.2609.07775","doi":"https://doi.org/10.48550/arxiv.2609.07775","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.07775","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:2609.07775","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.07775","pdf_url":"https://arxiv.org/pdf/2609.07775","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":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212010880.pdf","grobid_xml":"https://content.openalex.org/works/W7212010880.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1553677037","https://openalex.org/W2964412079","https://openalex.org/W3026211942","https://openalex.org/W3119069281","https://openalex.org/W4293339315","https://openalex.org/W4300548556","https://openalex.org/W4316465046","https://openalex.org/W4353040692","https://openalex.org/W4385659419","https://openalex.org/W4385664556","https://openalex.org/W4387013354","https://openalex.org/W4400166569","https://openalex.org/W4411932271","https://openalex.org/W4414091885","https://openalex.org/W7118350688","https://openalex.org/W7120172569","https://openalex.org/W7125202184","https://openalex.org/W7127597504"],"related_works":["https://openalex.org/W7125202184","https://openalex.org/W4415318291","https://openalex.org/W3023961618","https://openalex.org/W4415311633","https://openalex.org/W4385664556","https://openalex.org/W2924800398","https://openalex.org/W7117574420","https://openalex.org/W7129032150","https://openalex.org/W6941086587","https://openalex.org/W4293574970"],"abstract_inverted_index":{"Despite":[0],"the":[1,38,44,65,70,84,127,130,180],"exhaustive":[2],"understanding":[3],"gathered":[4],"around":[5],"non-interacting":[6,165],"topological":[7,23,77,166],"states":[8],"of":[9,17,69,86,94,129,182,186],"matter,":[10],"there":[11],"is":[12,26],"no":[13,152],"single":[14],"method":[15],"capable":[16],"systematically":[18],"delivering":[19],"simple,":[20],"numerically":[21],"efficient":[22,101],"invariants":[24,115],"that":[25,123,136,141,150],"applicable":[27],"to":[28,79,98,102,162,176],"all":[29],"crystalline":[30,121,170],"and":[31,46,49,100,118,178],"non-crystalline":[32,172],"systems":[33],"alike.":[34],"Here":[35],"we":[36],"revisit":[37],"spectral":[39,131],"localizer":[40,132],"operator,":[41],"constructed":[42],"from":[43],"Hamiltonian":[45,61],"position":[47],"operators,":[48],"show":[50],"how":[51],"it":[52,56],"can":[53],"be":[54],"treated":[55],"as":[57,146,148],"an":[58,90],"auxiliary":[59],"zero-dimensional":[60],"whose":[62],"topology":[63,181],"encodes":[64],"higher":[66],"dimensional":[67],"phases":[68,122,140,149],"parent":[71],"Hamiltonian.":[72],"Its":[73],"classification":[74],"reduces":[75],"every":[76],"invariant":[78,120,167],"a":[80,87,159,169],"matrix":[81],"signature":[82],"or":[83,171],"sign":[85],"Pfaffian":[88],"for":[89,116,168],"appropriate":[91],"localizer,":[92],"both":[93],"which":[95],"are":[96],"simple":[97,113],"interpret":[99],"compute":[103],"in":[104],"real":[105],"space.":[106],"We":[107],"validate":[108],"this":[109],"approach":[110],"by":[111],"deriving":[112],"real-space":[114],"weak":[117],"rotationally":[119],"were":[124],"previously":[125,153,183],"beyond":[126],"grasp":[128],"formalism,":[133],"atomic":[134],"limits":[135],"escape":[137],"scattering":[138],"invariants,":[139],"evade":[142],"symmetry-based":[143],"indicator":[144],"methods,":[145],"well":[147],"had":[151],"known":[154],"invariant.":[155],"Our":[156],"work":[157],"provides":[158],"systematic":[160],"way":[161],"construct":[163],"any":[164],"systems,":[173],"opening":[174],"avenues":[175],"classify":[177],"predict":[179],"unexplored":[184],"classes":[185],"materials.":[187]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-10T00:00:00"}