{"id":"https://openalex.org/W7220454149","doi":"https://doi.org/10.48550/arxiv.2610.03557","title":"A graph-theoretic analysis of non-generic free-fermion solvability by Krylov decompositions","display_name":"A graph-theoretic analysis of non-generic free-fermion solvability by Krylov decompositions","publication_year":2026,"publication_date":"2026-10-02","ids":{"openalex":"https://openalex.org/W7220454149","doi":"https://doi.org/10.48550/arxiv.2610.03557"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.03557","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03557","pdf_url":"https://arxiv.org/pdf/2610.03557","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/2610.03557","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074587456","display_name":"Jannis Ruh","orcid":"https://orcid.org/0009-0004-9820-7348","observed_orcids":["https://orcid.org/0009-0004-9820-7348"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ruh, Jannis","raw_affiliation_strings":["Centre for Quantum Software and Information , School of Computer Science ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre for Quantum Software and Information , School of Computer Science ,","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080349035","display_name":"Samuel J. Elman","orcid":"https://orcid.org/0000-0003-2140-4787","observed_orcids":["https://orcid.org/0000-0003-2140-4787"]},"institutions":[{"id":"https://openalex.org/I114017466","display_name":"University of Technology Sydney","ror":"https://ror.org/03f0f6041","country_code":"AU","type":"education","lineage":["https://openalex.org/I114017466"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Elman, Samuel J.","raw_affiliation_strings":["Centre for Quantum Software and Information , School of Computer Science ,","Faculty of Engineering & Information Technology , University of Technology Sydney , NSW 2007 , Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre for Quantum Software and Information , School of Computer Science ,","institution_ids":[]},{"raw_affiliation_string":"Faculty of Engineering & Information Technology , University of Technology Sydney , NSW 2007 , Australia","institution_ids":["https://openalex.org/I114017466"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081141125","display_name":"Adrian Chapman","orcid":"https://orcid.org/0000-0003-2303-7589","observed_orcids":["https://orcid.org/0000-0003-2303-7589"]},"institutions":[{"id":"https://openalex.org/I4210126100","display_name":"Phasecraft Ltd. (United Kingdom)","ror":"https://ror.org/042jzp908","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210126100"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Chapman, Adrian","raw_affiliation_strings":["Phasecraft Ltd"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Phasecraft Ltd","institution_ids":["https://openalex.org/I4210126100"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"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":0.9854000210762024,"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":0.9854000210762024,"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":0.009200000204145908,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.001500000013038516,"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/induced-paths","display_name":"induced paths","score":0.7160000205039978},{"id":"https://openalex.org/keywords/gaussian-transformation","display_name":"Gaussian transformation","score":0.9729999899864197}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.72079998254776},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4912000000476837},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.48829999566078186},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.45010000467300415},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.43790000677108765},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4077000021934509},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3937999904155731},{"id":"https://openalex.org/C188971069","wikidata":"https://www.wikidata.org/wiki/Q1636734","display_name":"Universal algebra","level":3,"score":0.3878999948501587},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.3578999936580658},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35420000553131104},{"id":"https://openalex.org/C38710091","wikidata":"https://www.wikidata.org/wiki/Q192242","display_name":"Frustration","level":2,"score":0.34700000286102295},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3176000118255615},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.2953000068664551},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.29120001196861267},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.289900004863739},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.28619998693466187},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.2831000089645386},{"id":"https://openalex.org/C86524685","wikidata":"https://www.wikidata.org/wiki/Q273037","display_name":"Hamiltonian path","level":3,"score":0.2732999920845032},{"id":"https://openalex.org/C180347388","wikidata":"https://www.wikidata.org/wiki/Q336233","display_name":"Pauli matrices","level":2,"score":0.26739999651908875},{"id":"https://openalex.org/C110340908","wikidata":"https://www.wikidata.org/wiki/Q131594","display_name":"Pauli exclusion principle","level":2,"score":0.2612999975681305},{"id":"https://openalex.org/C64999384","wikidata":"https://www.wikidata.org/wiki/Q3507967","display_name":"Symmetrization","level":2,"score":0.25940001010894775},{"id":"https://openalex.org/C154018700","wikidata":"https://www.wikidata.org/wiki/Q898323","display_name":"Path integral formulation","level":3,"score":0.25760000944137573},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.25760000944137573}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.03557","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03557","pdf_url":"https://arxiv.org/pdf/2610.03557","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.2610.03557","doi":"https://doi.org/10.48550/arxiv.2610.03557","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.03557","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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.03557","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03557","pdf_url":"https://arxiv.org/pdf/2610.03557","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220454149.pdf","grobid_xml":"https://content.openalex.org/works/W7220454149.grobid-xml"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W1524834675","https://openalex.org/W1860626550","https://openalex.org/W1926418975","https://openalex.org/W1970941569","https://openalex.org/W2016311577","https://openalex.org/W2027003240","https://openalex.org/W2033430067","https://openalex.org/W2067355240","https://openalex.org/W2077464955","https://openalex.org/W2113582551","https://openalex.org/W2528841422","https://openalex.org/W2895217576","https://openalex.org/W2955374454","https://openalex.org/W2963624733","https://openalex.org/W3010726287","https://openalex.org/W3035925708","https://openalex.org/W3110909405","https://openalex.org/W3117932051","https://openalex.org/W3121160018","https://openalex.org/W4292662642","https://openalex.org/W4305038077","https://openalex.org/W4378498873","https://openalex.org/W4394692974","https://openalex.org/W4401306959","https://openalex.org/W4403587722","https://openalex.org/W4403814348","https://openalex.org/W4404097977","https://openalex.org/W4406169147","https://openalex.org/W4409317517","https://openalex.org/W4409468966","https://openalex.org/W4409731064","https://openalex.org/W4414349340","https://openalex.org/W4414385031","https://openalex.org/W4415191379","https://openalex.org/W4416830875","https://openalex.org/W7140189768","https://openalex.org/W7162802278","https://openalex.org/W7163076652","https://openalex.org/W7163910413","https://openalex.org/W7167681211"],"related_works":["https://openalex.org/W4378498873","https://openalex.org/W3110909405","https://openalex.org/W7163076652","https://openalex.org/W4409731064","https://openalex.org/W7167681211","https://openalex.org/W4415191379","https://openalex.org/W7127592295","https://openalex.org/W7164001743","https://openalex.org/W4292662642","https://openalex.org/W7213222349"],"abstract_inverted_index":{"Exactly":[0],"solvable":[1,54,117,198],"models":[2,35,55,74],"are":[3,17,99,123,136],"often":[4],"identified":[5],"from":[6],"structural":[7],"features":[8],"of":[9,23,33,46,72,77,84,93,115,132,160,163,175,186],"their":[10,47],"interactions.":[11],"For":[12],"quantum":[13],"spin":[14,34],"Hamiltonians,":[15],"these":[16],"captured":[18],"by":[19],"the":[20,120,126,130,143,164,171],"frustration":[21,28,165],"graph":[22,29,78,166],"anticommuting":[24],"Pauli":[25],"terms.":[26],"The":[27],"characterizes":[30],"broad":[31],"families":[32],"that":[36,56,98,151,168],"map":[37],"to":[38,111,195],"free":[39],"fermions":[40],"for":[41,146],"arbitrary,":[42],"or":[43],"generic,":[44],"values":[45],"coupling":[48],"strengths.":[49],"Nevertheless,":[50],"there":[51],"exist":[52],"non-generically":[53,137],"admit":[57],"free-fermion":[58,116],"solutions":[59],"only":[60],"at":[61],"finely":[62],"tuned":[63],"couplings.":[64],"In":[65],"this":[66,133],"work,":[67],"we":[68,89],"characterize":[69],"a":[70,91,112,184,192],"family":[71,114,135],"such":[73],"in":[75,102,125,158],"terms":[76,159],"structures.":[79],"Given":[80],"an":[81,156],"arbitrary":[82],"instance":[83],"Fendley's":[85],"free-fermions-in-disguise":[86],"(FFD)":[87],"chain,":[88],"construct":[90],"set":[92],"operators,":[94],"called":[95],"Krylov":[96,121,153],"currents,":[97],"exactly":[100,197],"quadratic":[101],"its":[103],"effective":[104],"fermionic":[105],"modes":[106],"and":[107,139,167,189],"thus":[108],"extend":[109],"it":[110],"linear":[113],"Hamiltonians.":[118,200],"As":[119],"currents":[122],"nonlinear":[124],"FFD":[127],"Hamiltonian":[128],"terms,":[129],"elements":[131],"generated":[134],"solvable,":[138],"they":[140,169,190],"accordingly":[141],"fail":[142],"known":[144],"conditions":[145],"generic":[147],"solvability.":[148],"We":[149],"prove":[150],"every":[152],"current":[154],"admits":[155],"expansion":[157],"induced":[161],"paths":[162],"generate":[170],"full":[172],"special-orthogonal":[173],"algebra":[174],"Gaussian":[176],"transformations.":[177],"Our":[178],"results":[179],"identify":[180],"path":[181],"support":[182],"as":[183],"signature":[185],"non-generic":[187],"solvability,":[188],"provide":[191],"systematic":[193],"route":[194],"finding":[196],"many-body":[199]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-06T00:00:00"}
