{"id":"https://openalex.org/W3217159017","doi":"https://doi.org/10.21468/scipostphys.14.4.085","title":"Simulating thermal density operators with cluster expansions and tensor networks","display_name":"Simulating thermal density operators with cluster expansions and tensor networks","publication_year":2023,"publication_date":"2023-04-26","ids":{"openalex":"https://openalex.org/W3217159017","doi":"https://doi.org/10.21468/scipostphys.14.4.085","mag":"3217159017"},"language":"en","primary_location":{"id":"doi:10.21468/scipostphys.14.4.085","doi":"https://doi.org/10.21468/scipostphys.14.4.085","is_oa":true,"landing_page_url":"https://doi.org/10.21468/scipostphys.14.4.085","pdf_url":"https://scipost.org/10.21468/SciPostPhys.14.4.085/pdf","source":{"id":"https://openalex.org/S4210195687","display_name":"SciPost Physics","issn_l":"2542-4653","issn":["2542-4653"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","ddh","doaj","dongbi-b","jufo-1","norway-1","oarl","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310318585","host_organization_name":"SciPost.org","host_organization_lineage":["https://openalex.org/P4310318585"],"host_organization_lineage_names":["SciPost.org"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SciPost Physics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://scipost.org/10.21468/SciPostPhys.14.4.085/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016666918","display_name":"Bram Vanhecke","orcid":"https://orcid.org/0000-0001-9557-1591","observed_orcids":["https://orcid.org/0000-0001-9557-1591"]},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]},{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["AT","BE"],"is_corresponding":false,"raw_author_name":"Bram Vanhecke","raw_affiliation_strings":["Ghent University","University of Vienna","Department of Physics and Astronomy, University of Ghent, Krijgslaan 281, 9000 Gent, Belgium","University of Vienna, Faculty of Physics, Boltzmanngasse 5, 1090 Wien, Austria"],"raw_orcid":"https://orcid.org/0000-0001-9557-1591","affiliations":[{"raw_affiliation_string":"Ghent University","institution_ids":["https://openalex.org/I32597200"]},{"raw_affiliation_string":"University of Vienna","institution_ids":["https://openalex.org/I129774422"]},{"raw_affiliation_string":"Department of Physics and Astronomy, University of Ghent, Krijgslaan 281, 9000 Gent, Belgium","institution_ids":["https://openalex.org/I32597200"]},{"raw_affiliation_string":"University of Vienna, Faculty of Physics, Boltzmanngasse 5, 1090 Wien, Austria","institution_ids":["https://openalex.org/I129774422"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050252456","display_name":"David Devoogdt","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"David Devoogdt","raw_affiliation_strings":["Ghent University","Department of Physics and Astronomy, University of Ghent, Krijgslaan 281, 9000 Gent, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ghent University","institution_ids":["https://openalex.org/I32597200"]},{"raw_affiliation_string":"Department of Physics and Astronomy, University of Ghent, Krijgslaan 281, 9000 Gent, Belgium","institution_ids":["https://openalex.org/I32597200"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001154267","display_name":"Frank Verstraete","orcid":"https://orcid.org/0000-0003-0270-5592","observed_orcids":["https://orcid.org/0000-0003-0270-5592","https://orcid.org/0009-0002-3157-7104"]},"institutions":[{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Frank Verstraete","raw_affiliation_strings":["Ghent University","Department of Physics and Astronomy, University of Ghent, Krijgslaan 281, 9000 Gent, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ghent University","institution_ids":["https://openalex.org/I32597200"]},{"raw_affiliation_string":"Department of Physics and Astronomy, University of Ghent, Krijgslaan 281, 9000 Gent, Belgium","institution_ids":["https://openalex.org/I32597200"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065903932","display_name":"Laurens Vanderstraeten","orcid":"https://orcid.org/0000-0002-3227-9822","observed_orcids":["https://orcid.org/0000-0002-3227-9822"]},"institutions":[{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Laurens Vanderstraeten","raw_affiliation_strings":["Ghent University","Department of Physics and Astronomy, University of Ghent, Krijgslaan 281, 9000 Gent, Belgium"],"raw_orcid":"https://orcid.org/0000-0002-3227-9822","affiliations":[{"raw_affiliation_string":"Ghent University","institution_ids":["https://openalex.org/I32597200"]},{"raw_affiliation_string":"Department of Physics and Astronomy, University of Ghent, Krijgslaan 281, 9000 Gent, Belgium","institution_ids":["https://openalex.org/I32597200"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.008,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.70415512,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"14","issue":"4","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":0.9994999766349792,"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":0.9994999766349792,"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/T10591","display_name":"Theoretical and Computational 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"}},{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.0,"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/cluster-expansion","display_name":"cluster expansion","score":0.8659999966621399},{"id":"https://openalex.org/keywords/quantum-spin-systems","display_name":"quantum spin systems","score":0.75},{"id":"https://openalex.org/keywords/transverse-field-ising-model","display_name":"transverse-field Ising model","score":0.8709999918937683},{"id":"https://openalex.org/keywords/square-lattice","display_name":"square lattice","score":0.9259999990463257},{"id":"https://openalex.org/keywords/thermal-phase-transition","display_name":"temperature-induced phase transition","score":0.9010000228881836},{"id":"https://openalex.org/keywords/critical-points","display_name":"critical points","score":0.6880000233650208},{"id":"https://openalex.org/keywords/universality-class","display_name":"universality class","score":0.9710000157356262},{"id":"https://openalex.org/keywords/imaginary-time-evolution","display_name":"imaginary time evolution","score":0.5699999928474426},{"id":"https://openalex.org/keywords/tensor-network-contraction","display_name":"tensor network contraction","score":0.6330000162124634},{"id":"https://openalex.org/keywords/one-dimensional-systems","display_name":"one-dimensional systems","score":0.6690000295639038}],"concepts":[{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.680561900138855},{"id":"https://openalex.org/C2778999785","wikidata":"https://www.wikidata.org/wiki/Q5136697","display_name":"Cluster expansion","level":2,"score":0.6031287908554077},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.5517829656600952},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5380468368530273},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5335942506790161},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.5209011435508728},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.493294894695282},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.465247243642807},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.4577959179878235},{"id":"https://openalex.org/C19637589","wikidata":"https://www.wikidata.org/wiki/Q1117940","display_name":"Coupled cluster","level":3,"score":0.42985472083091736},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33562809228897095},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.30407923460006714},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1799108386039734},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12107154726982117},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.09386658668518066},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C32909587","wikidata":"https://www.wikidata.org/wiki/Q11369","display_name":"Molecule","level":2,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.21468/scipostphys.14.4.085","doi":"https://doi.org/10.21468/scipostphys.14.4.085","is_oa":true,"landing_page_url":"https://doi.org/10.21468/scipostphys.14.4.085","pdf_url":"https://scipost.org/10.21468/SciPostPhys.14.4.085/pdf","source":{"id":"https://openalex.org/S4210195687","display_name":"SciPost Physics","issn_l":"2542-4653","issn":["2542-4653"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","ddh","doaj","dongbi-b","jufo-1","norway-1","oarl","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310318585","host_organization_name":"SciPost.org","host_organization_lineage":["https://openalex.org/P4310318585"],"host_organization_lineage_names":["SciPost.org"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SciPost Physics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2112.01507","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2112.01507","pdf_url":"https://arxiv.org/pdf/2112.01507","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:doaj.org/article:90ecc9889ebe431387139a05bcb0233a","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/90ecc9889ebe431387139a05bcb0233a","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SciPost Physics, Vol 14, Iss 4, p 085 (2023)","raw_type":"article"},{"id":"doi:10.48550/arxiv.2112.01507","doi":"https://doi.org/10.48550/arxiv.2112.01507","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2112.01507","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":"doi:10.21468/scipostphys.14.4.085","doi":"https://doi.org/10.21468/scipostphys.14.4.085","is_oa":true,"landing_page_url":"https://doi.org/10.21468/scipostphys.14.4.085","pdf_url":"https://scipost.org/10.21468/SciPostPhys.14.4.085/pdf","source":{"id":"https://openalex.org/S4210195687","display_name":"SciPost Physics","issn_l":"2542-4653","issn":["2542-4653"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","ddh","doaj","dongbi-b","jufo-1","norway-1","oarl","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310318585","host_organization_name":"SciPost.org","host_organization_lineage":["https://openalex.org/P4310318585"],"host_organization_lineage_names":["SciPost.org"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SciPost Physics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G8923609168","display_name":null,"funder_award_id":"647905","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"}],"funders":[{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"},{"id":"https://openalex.org/F4320327336","display_name":"Vlaamse regering","ror":null},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3217159017.pdf","grobid_xml":"https://content.openalex.org/works/W3217159017.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1528226895","https://openalex.org/W1531177993","https://openalex.org/W1860740507","https://openalex.org/W1930886120","https://openalex.org/W1969631049","https://openalex.org/W1973224679","https://openalex.org/W1990455780","https://openalex.org/W1991918076","https://openalex.org/W1997126380","https://openalex.org/W2014237348","https://openalex.org/W2039434005","https://openalex.org/W2049415658","https://openalex.org/W2054647191","https://openalex.org/W2068894496","https://openalex.org/W2070162907","https://openalex.org/W2090558939","https://openalex.org/W2140788376","https://openalex.org/W2167325579","https://openalex.org/W2256107619","https://openalex.org/W2581056149","https://openalex.org/W2607068097","https://openalex.org/W2770729026","https://openalex.org/W2896714001","https://openalex.org/W2901089295","https://openalex.org/W2932831793","https://openalex.org/W2963469706","https://openalex.org/W2995763982","https://openalex.org/W3093085120","https://openalex.org/W4251024638"],"related_works":["https://openalex.org/W2995763982","https://openalex.org/W7131643197","https://openalex.org/W4414977960","https://openalex.org/W2512476273","https://openalex.org/W2599512248","https://openalex.org/W2782498983","https://openalex.org/W3021348370","https://openalex.org/W3172313137","https://openalex.org/W3166811422","https://openalex.org/W6967124287"],"abstract_inverted_index":{"We":[0,23,48,86],"provide":[1],"an":[2],"efficient":[3],"approximation":[4,39,114],"for":[5,32,42,52,82],"the":[6,38,54,91,96,101,112,123,129,132,140],"exponential":[7],"of":[8,19,58,95,131,139],"a":[9,20,59,65,69,108,118],"local":[10],"operator":[11,29,57],"in":[12,122],"quantum":[13,61],"spin":[14,62],"systems":[15],"using":[16],"tensor-network":[17],"representations":[18],"cluster":[21,26,71,133],"expansion.":[22],"benchmark":[24],"this":[25,50,88],"tensor":[27,84],"network":[28],"(cluster":[30],"TNO)":[31],"one-dimensional":[33],"systems,":[34],"and":[35,104],"show":[36],"that":[37,111],"works":[40],"well":[41],"large":[43],"real-":[44],"or":[45],"imaginary-time":[46],"steps.":[47],"use":[49],"formalism":[51],"representing":[53],"thermal":[55,92],"density":[56],"two-dimensional":[60,83],"system":[63],"at":[64],"certain":[66],"temperature":[67],"as":[68],"single":[70],"TNO,":[72],"which":[73],"we":[74,105,135],"can":[75],"then":[76],"contract":[77],"by":[78,127],"standard":[79],"contraction":[80],"methods":[81],"networks.":[85],"apply":[87],"approach":[89],"to":[90,117,144],"phase":[93,120],"transition":[94,121],"transverse-field":[97],"Ising":[98],"model":[99],"on":[100],"square":[102],"lattice,":[103],"find":[106,136],"through":[107],"scaling":[109],"analysis":[110],"cluster-TNO":[113],"gives":[115],"rise":[116],"continuous":[119],"correct":[124],"universality":[125],"class;":[126],"increasing":[128],"order":[130],"expansion":[134],"good":[137],"values":[138],"critical":[141],"point":[142],"up":[143],"surprisingly":[145],"low":[146],"temperatures.":[147]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2021-12-06T00:00:00"}