{"id":"https://openalex.org/W7214101381","doi":"https://doi.org/10.48550/arxiv.2609.25276","title":"Finite-state automata for exact matrix product operators of tight-binding Hamiltonians: fractals, quasicrystals, trees and hyperbolic lattices","display_name":"Finite-state automata for exact matrix product operators of tight-binding Hamiltonians: fractals, quasicrystals, trees and hyperbolic lattices","publication_year":2026,"publication_date":"2026-09-21","ids":{"openalex":"https://openalex.org/W7214101381","doi":"https://doi.org/10.48550/arxiv.2609.25276"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.25276","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25276","pdf_url":"https://arxiv.org/pdf/2609.25276","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.25276","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088934814","display_name":"Marta Brzezi\u0144ska","orcid":"https://orcid.org/0000-0003-0657-4382","observed_orcids":["https://orcid.org/0000-0003-0657-4382"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Brzezi\u0144ska, Marta","raw_affiliation_strings":["1 Quobly , 38000 Grenoble , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"1 Quobly , 38000 Grenoble , France","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065512558","display_name":"Jeanne Colbois","orcid":"https://orcid.org/0000-0002-5495-9466","observed_orcids":["https://orcid.org/0000-0002-5495-9466"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210144791","display_name":"Institut N\u00e9el","ror":"https://ror.org/04dbzz632","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210098836","https://openalex.org/I4210144791","https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Colbois, Jeanne","raw_affiliation_strings":["Univ. Grenoble Alpes , CNRS , Institut N\u00e9el , 38000 Grenoble , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. Grenoble Alpes , CNRS , Institut N\u00e9el , 38000 Grenoble , France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210144791"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003664373","display_name":"Lo\u00efc Herviou","orcid":"https://orcid.org/0000-0003-4220-8785","observed_orcids":["https://orcid.org/0000-0003-4220-8785"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210119139","display_name":"Laboratoire de Physique et Mod\u00e9lisation des Milieux Condens\u00e9s","ror":"https://ror.org/02mc6qk71","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210098836","https://openalex.org/I4210119139","https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Herviou, Lo\u00efc","raw_affiliation_strings":["Univ. Grenoble Alpes , CNRS , LPMMC , 38000 Grenoble , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. Grenoble Alpes , CNRS , LPMMC , 38000 Grenoble , France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210119139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"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/T11804","display_name":"Quantum many-body systems","score":0.9970999956130981,"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":0.9970999956130981,"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/T11887","display_name":"Quasicrystal Structures and Properties","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.00019999999494757503,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/matrix-product-operators","display_name":"matrix product operators","score":0.9900000095367432},{"id":"https://openalex.org/keywords/finite-state-machines","display_name":"finite automata","score":0.9079999923706055},{"id":"https://openalex.org/keywords/tight-binding-hamiltonian","display_name":"tight-binding Hamiltonian","score":0.9950000047683716},{"id":"https://openalex.org/keywords/tensor-networks","display_name":"tensor networks","score":0.6420000195503235},{"id":"https://openalex.org/keywords/fractals","display_name":"fractals","score":0.765999972820282},{"id":"https://openalex.org/keywords/quasicrystals","display_name":"quasicrystals","score":0.8659999966621399},{"id":"https://openalex.org/keywords/fibonacci-quasicrystals","display_name":"Fibonacci quasicrystals","score":0.9580000042915344},{"id":"https://openalex.org/keywords/cayley-tree","display_name":"Cayley tree","score":0.9890000224113464},{"id":"https://openalex.org/keywords/hyperbolic-lattices","display_name":"hyperbolic lattices","score":1.0},{"id":"https://openalex.org/keywords/kernel-polynomial-method","display_name":"kernel polynomial method","score":0.8370000123977661},{"id":"https://openalex.org/keywords/electronic-structure","display_name":"electronic structure","score":0.4259999990463257},{"id":"https://openalex.org/keywords/spectral-properties","display_name":"spectral properties","score":0.6140000224113464}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6577000021934509},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.6367999911308289},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.47690001130104065},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4659999907016754},{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.43619999289512634},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4169999957084656},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.414000004529953},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4023999869823456},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40119999647140503},{"id":"https://openalex.org/C2778351468","wikidata":"https://www.wikidata.org/wiki/Q17149634","display_name":"Matrix product state","level":4,"score":0.399399995803833},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3767000138759613},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.34769999980926514},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34450000524520874},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.3382999897003174},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3343000113964081},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.3294999897480011},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.323199987411499},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.32120001316070557},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.31130000948905945},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.3027999997138977},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.29030001163482666},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.26649999618530273},{"id":"https://openalex.org/C35527583","wikidata":"https://www.wikidata.org/wiki/Q189156","display_name":"Cellular automaton","level":2,"score":0.26589998602867126},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.25949999690055847},{"id":"https://openalex.org/C194525867","wikidata":"https://www.wikidata.org/wiki/Q5265707","display_name":"Deterministic automaton","level":3,"score":0.25839999318122864},{"id":"https://openalex.org/C181266644","wikidata":"https://www.wikidata.org/wiki/Q7318293","display_name":"Reversible cellular automaton","level":5,"score":0.2567000091075897},{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.2515999972820282}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2609.25276","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25276","pdf_url":"https://arxiv.org/pdf/2609.25276","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":"pmh:oai:HAL:hal-05774818v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-05774818","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2609.25276","doi":"https://doi.org/10.48550/arxiv.2609.25276","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.25276","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:2609.25276","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25276","pdf_url":"https://arxiv.org/pdf/2609.25276","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/G4030236852","display_name":"Tensor networks for the fractional quantum Hall effect","funder_award_id":"ANR-25-CE30-2205","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214101381.pdf","grobid_xml":"https://content.openalex.org/works/W7214101381.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2999753305","https://openalex.org/W2768739926","https://openalex.org/W7100411698","https://openalex.org/W3033779131","https://openalex.org/W7167049807","https://openalex.org/W2065506039","https://openalex.org/W4283643672","https://openalex.org/W2014237348","https://openalex.org/W7114784977","https://openalex.org/W2572028881"],"abstract_inverted_index":{"Inspired":[0],"by":[1,82],"the":[2,6,41,63,66,73,77,83,91,94,111,127,136],"recent":[3],"progress":[4],"in":[5,44],"simulation":[7],"of":[8,35,62,68,85,93,121,138,145],"tight-binding":[9],"Hamiltonians":[10,28],"on":[11,29],"large":[12,149],"lattices":[13,146],"using":[14],"tensor":[15,53],"networks,":[16,54],"we":[17,39],"introduce":[18],"a":[19,45,132,142],"systematic":[20],"matrix":[21],"product":[22],"operator":[23],"(MPO)":[24],"construction":[25],"for":[26],"single-particle":[27],"recursively":[30],"structured":[31],"lattices.":[32],"Taking":[33],"advantage":[34],"this":[36],"recursive":[37],"structure,":[38],"encode":[40],"lattice":[42],"geometry":[43],"finite-state":[46],"automaton":[47,86],"and,":[48],"adapting":[49],"ideas":[50],"from":[51],"Abelian-symmetric":[52],"obtain":[55],"an":[56],"exact":[57],"and":[58,76,103,105],"analytical":[59],"MPO":[60,116],"representation":[61],"Hamiltonian,":[64],"where":[65],"number":[67,84],"tensors":[69],"grows":[70],"logarithmically":[71],"with":[72,110],"system":[74,150],"size":[75],"bond":[78],"dimension":[79],"is":[80],"set":[81],"states.":[87],"Several":[88],"examples":[89],"demonstrate":[90],"generality":[92],"framework:":[95],"regular":[96],"lattices,":[97,102],"fractals,":[98],"Cayley":[99],"trees,":[100],"hyperbolic":[101],"one-":[104],"two-dimensional":[106],"Fibonacci":[107],"quasicrystals.":[108],"Combined":[109],"kernel":[112],"polynomial":[113],"method,":[114],"these":[115],"representations":[117],"enable":[118],"large-scale":[119],"calculations":[120],"spectral":[122],"properties":[123,140],"without":[124],"explicitly":[125],"constructing":[126],"full":[128],"Hamiltonian.":[129],"This":[130],"provides":[131],"unified":[133],"route":[134],"to":[135],"exploration":[137],"electronic":[139],"across":[141],"broad":[143],"class":[144],"at":[147],"exponentially":[148],"sizes.":[151]},"counts_by_year":[],"updated_date":"2026-10-25T09:29:13.331239","created_date":"2026-09-24T00:00:00"}
