{"id":"https://openalex.org/W7214909884","doi":"https://doi.org/10.48550/arxiv.2609.37814","title":"Hierarchical Fourier Phase Projection for Local Electronic Observables","display_name":"Hierarchical Fourier Phase Projection for Local Electronic Observables","publication_year":2026,"publication_date":"2026-09-29","ids":{"openalex":"https://openalex.org/W7214909884","doi":"https://doi.org/10.48550/arxiv.2609.37814"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.37814","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37814","pdf_url":"https://arxiv.org/pdf/2609.37814","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/2609.37814","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153658539","display_name":"Tao Hu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hu, Tao","raw_affiliation_strings":["Key Laboratory of Artificial Micro-and Nano-Structures of Ministry of Education and School of Physics and Technology , Wuhan University , Wuhan 430072 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Artificial Micro-and Nano-Structures of Ministry of Education and School of Physics and Technology , Wuhan University , Wuhan 430072 , China","institution_ids":["https://openalex.org/I37461747"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5153580670","display_name":"Weiqing Zhou","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]},{"id":"https://openalex.org/I4405270616","display_name":"Wuhan Institute of Quantum Technology","ror":"https://ror.org/011a6ea26","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4405270616"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhou, Weiqing","raw_affiliation_strings":["Key Laboratory of Artificial Micro-and Nano-Structures of Ministry of Education and School of Physics and Technology , Wuhan University , Wuhan 430072 , China","Wuhan Institute of Quantum Technology , Wuhan 430206 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Artificial Micro-and Nano-Structures of Ministry of Education and School of Physics and Technology , Wuhan University , Wuhan 430072 , China","institution_ids":["https://openalex.org/I37461747"]},{"raw_affiliation_string":"Wuhan Institute of Quantum Technology , Wuhan 430206 , China","institution_ids":["https://openalex.org/I4405270616"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5153654212","display_name":"Zhichang Fu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fu, Zhichang","raw_affiliation_strings":["Key Laboratory of Artificial Micro-and Nano-Structures of Ministry of Education and School of Physics and Technology , Wuhan University , Wuhan 430072 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Artificial Micro-and Nano-Structures of Ministry of Education and School of Physics and Technology , Wuhan University , Wuhan 430072 , China","institution_ids":["https://openalex.org/I37461747"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5153565125","display_name":"Yechen Chen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chen, Yechen","raw_affiliation_strings":["Key Laboratory of Artificial Micro-and Nano-Structures of Ministry of Education and School of Physics and Technology , Wuhan University , Wuhan 430072 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Artificial Micro-and Nano-Structures of Ministry of Education and School of Physics and Technology , Wuhan University , Wuhan 430072 , China","institution_ids":["https://openalex.org/I37461747"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5153644468","display_name":"Shengjun Yuan","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yuan, Shengjun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"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/T10002","display_name":"Advanced Chemical Physics Studies","score":0.9907000064849854,"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/T10002","display_name":"Advanced Chemical Physics Studies","score":0.9907000064849854,"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.00139999995008111,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10037","display_name":"Physics of Superconductivity and Magnetism","score":0.0007999999797903001,"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/error-estimation","display_name":"error estimation","score":0.7139999866485596},{"id":"https://openalex.org/keywords/electron-density","display_name":"electron density","score":0.765999972820282},{"id":"https://openalex.org/keywords/kohn-sham-hamiltonian","display_name":"Kohn-Sham Hamiltonian","score":0.9190000295639038},{"id":"https://openalex.org/keywords/convergence-acceleration","display_name":"convergence acceleration","score":0.5329999923706055}],"concepts":[{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.819100022315979},{"id":"https://openalex.org/C4069607","wikidata":"https://www.wikidata.org/wiki/Q868732","display_name":"Aliasing","level":3,"score":0.705299973487854},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.616599977016449},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.597599983215332},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.5220999717712402},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.510200023651123},{"id":"https://openalex.org/C132378524","wikidata":"https://www.wikidata.org/wiki/Q769463","display_name":"Pseudopotential","level":2,"score":0.4909000098705292},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.48019999265670776},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4763999879360199},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42730000615119934},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4255000054836273},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.4244999885559082},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.39149999618530273},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.3806000053882599},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.38029998540878296},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3637000024318695},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.36329999566078186},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3447999954223633},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.3416999876499176},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.335099995136261},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.3264999985694885},{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.31709998846054077},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.3052000105381012},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.303600013256073},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.2985999882221222},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28780001401901245},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2824000120162964},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.2800999879837036},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2793999910354614},{"id":"https://openalex.org/C81793267","wikidata":"https://www.wikidata.org/wiki/Q7180962","display_name":"Phase retrieval","level":3,"score":0.2732999920845032},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.2646999955177307},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.2614000141620636},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.26030001044273376},{"id":"https://openalex.org/C86025842","wikidata":"https://www.wikidata.org/wiki/Q5358432","display_name":"Electronic structure","level":2,"score":0.25459998846054077},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.2533999979496002},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.25099998712539673}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.37814","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37814","pdf_url":"https://arxiv.org/pdf/2609.37814","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.2609.37814","doi":"https://doi.org/10.48550/arxiv.2609.37814","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.37814","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:2609.37814","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37814","pdf_url":"https://arxiv.org/pdf/2609.37814","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/G465544519","display_name":null,"funder_award_id":"12425407","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6151145709","display_name":null,"funder_award_id":"12547165","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324116","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214909884.pdf","grobid_xml":"https://content.openalex.org/works/W7214909884.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7161987309"],"related_works":["https://openalex.org/W2068725607","https://openalex.org/W2332262004","https://openalex.org/W2068101012","https://openalex.org/W1982991255","https://openalex.org/W1992701595","https://openalex.org/W3178589796","https://openalex.org/W329317821","https://openalex.org/W7169766483","https://openalex.org/W2009747790","https://openalex.org/W2473316284"],"abstract_inverted_index":{"In":[0,78],"this":[1],"letter,":[2],"we":[3,80],"develop":[4],"hierarchical":[5],"Fourier":[6,31],"phase":[7],"projection":[8],"(HPP)":[9],"for":[10,84,91,159,173],"the":[11,20,24,48,52,58,68,82,108,112,117,138,142,156,166],"calculation":[12],"of":[13,23,30,40,95,111,124,144],"local":[14,131,160],"electronic":[15],"observables.":[16],"The":[17,45,102,122],"method":[18,83],"couples":[19],"spatial":[21,109],"decay":[22,110],"density":[25,113,118],"matrix":[26,119],"with":[27,73],"a":[28,63,129,148],"hierarchy":[29],"probes,":[32],"improving":[33],"accuracy":[34,132],"through":[35],"refinement,":[36],"and":[37,87,98],"making":[38],"use":[39,62],"all":[41],"previously":[42],"evaluated":[43],"responses.":[44],"variation":[46],"in":[47,154],"calculated":[49],"observables":[50,161],"during":[51],"refinement":[53],"process":[54],"carries":[55],"information":[56],"on":[57,137],"residual":[59],"error.":[60],"We":[61],"locality-based":[64],"model":[65],"to":[66,127,165],"estimate":[67],"error":[69],"from":[70],"these":[71],"changes":[72],"no":[74],"extra":[75],"probing":[76],"calculations.":[77],"particular,":[79],"demonstrate":[81],"electron":[85],"densities":[86],"nonlocal":[88],"pseudopotential":[89],"forces":[90],"fixed":[92],"Kohn-Sham":[93],"Hamiltonians":[94],"semiconductors,":[96],"metals":[97],"thermally":[99],"perturbed":[100],"silica.":[101],"convergence":[103],"is":[104,120,133],"significantly":[105],"accelerated":[106],"by":[107],"matrix,":[114],"especially":[115],"if":[116],"short-ranged.":[121],"number":[123],"probes":[125],"necessary":[126],"achieve":[128],"specific":[130],"only":[134],"weakly":[135],"dependent":[136],"system":[139],"size":[140],"within":[141],"range":[143],"consideration.":[145],"HPP":[146],"provides":[147],"route":[149],"toward":[150],"linear-scaling":[151],"electronic-structure":[152],"calculations":[153],"which":[155],"computational":[157],"effort":[158],"can":[162],"be":[163],"matched":[164],"required":[167],"accuracy,":[168],"offering":[169],"an":[170],"error-aware":[171],"strategy":[172],"large-scale":[174],"first-principles":[175],"simulations.":[176]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-10-01T00:00:00"}