{"id":"https://openalex.org/W4387562585","doi":"https://doi.org/10.2140/pmp.2025.6.1507","title":"Low-temperature spectrum of the quantum transfer matrix of the XXZ chain in the massless regime","display_name":"Low-temperature spectrum of the quantum transfer matrix of the XXZ chain in the massless regime","publication_year":2025,"publication_date":"2025-11-03","ids":{"openalex":"https://openalex.org/W4387562585","doi":"https://doi.org/10.2140/pmp.2025.6.1507"},"language":"en","primary_location":{"id":"doi:10.2140/pmp.2025.6.1507","doi":"https://doi.org/10.2140/pmp.2025.6.1507","is_oa":true,"landing_page_url":"https://doi.org/10.2140/pmp.2025.6.1507","pdf_url":null,"source":{"id":"https://openalex.org/S4210215060","display_name":"Probability and Mathematical Physics","issn_l":"2690-0998","issn":["2690-0998","2690-1005"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310320446","host_organization_name":"Mathematical Sciences Publishers","host_organization_lineage":["https://openalex.org/P4310320446"],"host_organization_lineage_names":["Mathematical Sciences Publishers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Probability and Mathematical Physics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.2140/pmp.2025.6.1507","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028700195","display_name":"Saskia Faulmann","orcid":"https://orcid.org/0000-0002-4963-7307","observed_orcids":["https://orcid.org/0000-0002-4963-7307"]},"institutions":[{"id":"https://openalex.org/I167360494","display_name":"University of Wuppertal","ror":"https://ror.org/00613ak93","country_code":"DE","type":"education","lineage":["https://openalex.org/I167360494"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Saskia Faulmann","raw_affiliation_strings":["Fakult\u00e4t f\u00fcr Mathematik und Naturwissenschaften, Bergische Universit\u00e4t Wuppertal, 42119 Wuppertal, Germany","Bergische Universit\u00e4t Wuppertal (Gau\u00dfstra\u00dfe 20,  42119 Wuppertal - Germany)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Mathematik und Naturwissenschaften, Bergische Universit\u00e4t Wuppertal, 42119 Wuppertal, Germany","institution_ids":["https://openalex.org/I167360494"]},{"raw_affiliation_string":"Bergische Universit\u00e4t Wuppertal (Gau\u00dfstra\u00dfe 20,  42119 Wuppertal - Germany)","institution_ids":["https://openalex.org/I167360494"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007585477","display_name":"Frank G\u00f6hmann","orcid":"https://orcid.org/0000-0003-2626-1965","observed_orcids":["https://orcid.org/0000-0003-2626-1965"]},"institutions":[{"id":"https://openalex.org/I167360494","display_name":"University of Wuppertal","ror":"https://ror.org/00613ak93","country_code":"DE","type":"education","lineage":["https://openalex.org/I167360494"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Frank G\u00f6hmann","raw_affiliation_strings":["Fakult\u00e4t f\u00fcr Mathematik und Naturwissenschaften, Bergische Universit\u00e4t Wuppertal, 42119 Wuppertal, Germany","Bergische Universit\u00e4t Wuppertal (Gau\u00dfstra\u00dfe 20,  42119 Wuppertal - Germany)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Mathematik und Naturwissenschaften, Bergische Universit\u00e4t Wuppertal, 42119 Wuppertal, Germany","institution_ids":["https://openalex.org/I167360494"]},{"raw_affiliation_string":"Bergische Universit\u00e4t Wuppertal (Gau\u00dfstra\u00dfe 20,  42119 Wuppertal - Germany)","institution_ids":["https://openalex.org/I167360494"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024297659","display_name":"Karol Kajetan Kozlowski","orcid":"https://orcid.org/0000-0002-5861-6399","observed_orcids":["https://orcid.org/0000-0002-5861-6399"]},"institutions":[{"id":"https://openalex.org/I113428412","display_name":"\u00c9cole Normale Sup\u00e9rieure de Lyon","ror":"https://ror.org/04zmssz18","country_code":"FR","type":"education","lineage":["https://openalex.org/I113428412","https://openalex.org/I203339264"]},{"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/I4210096929","display_name":"Laboratoire de Physique de l'ENS de Lyon","ror":"https://ror.org/00w5ay796","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I112936343","https://openalex.org/I113428412","https://openalex.org/I1294671590","https://openalex.org/I203339264","https://openalex.org/I4210096929","https://openalex.org/I4405259976","https://openalex.org/I4405263940","https://openalex.org/I48430043"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Karol K. Kozlowski","raw_affiliation_strings":["ENSL, CNRS, Laboratoire de Physique, 69342 Lyon, France","Phys-ENS - Laboratoire de Physique de l'ENS Lyon (46 all\u00e9e d'Italie 69007 Lyon - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ENSL, CNRS, Laboratoire de Physique, 69342 Lyon, France","institution_ids":["https://openalex.org/I113428412","https://openalex.org/I1294671590","https://openalex.org/I4210096929"]},{"raw_affiliation_string":"Phys-ENS - Laboratoire de Physique de l'ENS Lyon (46 all\u00e9e d'Italie 69007 Lyon - France)","institution_ids":["https://openalex.org/I4210096929"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.00113224,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"6","issue":"4","first_page":"1507","last_page":"1658"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":0.9672999978065491,"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":0.9672999978065491,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.01860000006854534,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.0027000000700354576,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/quantum-transfer-matrix","display_name":"quantum transfer matrix","score":0.8970000147819519},{"id":"https://openalex.org/keywords/xxz-spin-chain","display_name":"XXZ spin chain","score":0.8619999885559082},{"id":"https://openalex.org/keywords/integrable-systems","display_name":"integrable systems","score":0.5600000023841858},{"id":"https://openalex.org/keywords/bethe-ansatz","display_name":"Bethe ansatz","score":0.6460000276565552}],"concepts":[{"id":"https://openalex.org/C54937798","wikidata":"https://www.wikidata.org/wiki/Q2024141","display_name":"Massless particle","level":2,"score":0.8135312795639038},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.6068946123123169},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5976505279541016},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.5840920805931091},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5446668267250061},{"id":"https://openalex.org/C122890649","wikidata":"https://www.wikidata.org/wiki/Q7834016","display_name":"Transfer matrix","level":2,"score":0.5382158160209656},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5226166844367981},{"id":"https://openalex.org/C3079626","wikidata":"https://www.wikidata.org/wiki/Q234881","display_name":"Quantum electrodynamics","level":1,"score":0.38707271218299866},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3779486417770386},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3691525161266327},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.18496638536453247},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05129256844520569},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.2140/pmp.2025.6.1507","doi":"https://doi.org/10.2140/pmp.2025.6.1507","is_oa":true,"landing_page_url":"https://doi.org/10.2140/pmp.2025.6.1507","pdf_url":null,"source":{"id":"https://openalex.org/S4210215060","display_name":"Probability and Mathematical Physics","issn_l":"2690-0998","issn":["2690-0998","2690-1005"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310320446","host_organization_name":"Mathematical Sciences Publishers","host_organization_lineage":["https://openalex.org/P4310320446"],"host_organization_lineage_names":["Mathematical Sciences Publishers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Probability and Mathematical Physics","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04238918v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-04238918","pdf_url":"http://arxiv.org/pdf/2305.06679","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2023","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:oai:arXiv.org:2305.06679","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2305.06679","pdf_url":"https://arxiv.org/pdf/2305.06679","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-05760691v1","doi":null,"is_oa":false,"landing_page_url":"https://hal.science/hal-05760691","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Probability and Mathematical Physics, 2025, 6 (4), pp.1507-1658. &#x27E8;10.2140/pmp.2025.6.1507&#x27E9;","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.2305.06679","doi":"https://doi.org/10.48550/arxiv.2305.06679","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2305.06679","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:10.2140/pmp.2025.6.1507","doi":"https://doi.org/10.2140/pmp.2025.6.1507","is_oa":true,"landing_page_url":"https://doi.org/10.2140/pmp.2025.6.1507","pdf_url":null,"source":{"id":"https://openalex.org/S4210215060","display_name":"Probability and Mathematical Physics","issn_l":"2690-0998","issn":["2690-0998","2690-1005"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310320446","host_organization_name":"Mathematical Sciences Publishers","host_organization_lineage":["https://openalex.org/P4310320446"],"host_organization_lineage_names":["Mathematical Sciences Publishers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Probability and Mathematical Physics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1656604150","display_name":null,"funder_award_id":"FOR 2316","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G202495085","display_name":null,"funder_award_id":"1440140","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G3223231094","display_name":null,"funder_award_id":"PICS07877","funder_id":"https://openalex.org/F4320322892","funder_display_name":"Centre National de la Recherche Scientifique"},{"id":"https://openalex.org/G7308520682","display_name":null,"funder_award_id":"884584","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7636485559","display_name":null,"funder_award_id":"ERC-2019-ADG","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G811546825","display_name":"Mathematical Sciences Research Institute (MSRI)","funder_award_id":"1440140","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320322892","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1974784890","https://openalex.org/W1995670128","https://openalex.org/W1996572322","https://openalex.org/W2003666747","https://openalex.org/W2008821005","https://openalex.org/W2011426642","https://openalex.org/W2023953089","https://openalex.org/W2026841374","https://openalex.org/W2028546484","https://openalex.org/W2035653403","https://openalex.org/W2047077077","https://openalex.org/W2047523273","https://openalex.org/W2056318822","https://openalex.org/W2056719116","https://openalex.org/W2057190456","https://openalex.org/W2060280176","https://openalex.org/W2078953832","https://openalex.org/W2091468921","https://openalex.org/W2094264521","https://openalex.org/W2122384985","https://openalex.org/W2151091453","https://openalex.org/W2227313626","https://openalex.org/W2317586084","https://openalex.org/W2914926972","https://openalex.org/W2963955012"],"related_works":["https://openalex.org/W2140127851","https://openalex.org/W7098763745","https://openalex.org/W2914926972","https://openalex.org/W2026812935","https://openalex.org/W1984606386","https://openalex.org/W3014101470","https://openalex.org/W2049287381","https://openalex.org/W2076549361","https://openalex.org/W2401361692","https://openalex.org/W2047523273"],"abstract_inverted_index":{"The":[0],"free":[1,279],"energy":[2],"per":[3],"lattice":[4],"site":[5],"of":[6,22,42,49,62,72,87,112,116,154,160,186,207,217,247,277],"a":[7,18,88,102,135,143,288],"quantum":[8,25,36,51,163,204,219],"spin":[9,37,121,164],"chain":[10,122,165],"in":[11,28,91,166,172,237,264,292],"the":[12,29,43,50,63,70,73,85,92,98,113,120,158,161,167,173,179,184,187,190,198,203,218,227,238,244,248,253,265,271,275,278,293],"thermodynamic":[13],"limit":[14,267],"is":[15,101,224],"determined":[16],"by":[17,60,132,274],"single":[19],"`dominant'":[20],"Eigenvalue":[21,255],"an":[23,46],"associated":[24],"transfer":[26,52,205,220],"matrix":[27,53,206,221],"infinite":[30,239],"Trotter":[31,240],"number":[32,241],"limit.":[33,175,242],"For":[34],"integrable":[35],"chains,":[38],"related":[39,225],"with":[40,157],"solutions":[41,188],"Yang-Baxter":[44],"equation,":[45],"appropriate":[47],"choice":[48],"enables":[54],"to":[55,78,189,197,213,226,235,270],"study":[56,79],"its":[57,68,80],"spectrum,":[58],"e.g.\\":[59],"means":[61],"algebraic":[64],"Bethe":[65,199,228],"Ansatz.":[66],"In":[67,147],"turn,":[69],"knowledge":[71],"full":[74,99],"spectrum":[75,90,100,222,249,276],"allows":[76,211],"one":[77],"universality":[81],"properties":[82],"such":[83],"as":[84],"appearance":[86],"conformal":[89,282],"low-temperature":[93,174,266],"regime.":[94],"More":[95],"generally,":[96],"accessing":[97],"necessary":[103],"step":[104],"for":[105,119,142,202],"deriving":[106],"thermal":[107],"form":[108,185],"factor":[109],"series":[110],"representations":[111],"correlation":[114],"functions":[115],"local":[117],"operators":[118],"under":[123],"consideration.":[124],"These":[125],"are":[126,140,195,268],"statements":[127],"that":[128,139,194,215,223,231,258,262],"have":[129],"been":[130],"established":[131],"physicists":[133],"on":[134],"heuristic":[136],"level":[137],"and":[138,171,182,230,256],"calling":[141],"rigorous":[144],"mathematical":[145],"justification.":[146],"this":[148,155,208],"work":[149],"we":[150,250],"implement":[151],"certain":[152],"aspects":[153],"programme":[156],"example":[159],"XXZ":[162],"antiferromagnetic":[168],"massless":[169],"regime":[170],"We":[176],"rigorously":[177,251,286],"establish":[178],"existence,":[180],"uniqueness":[181],"characterise":[183],"non-linear":[191],"integral":[192],"equations":[193,201],"equivalent":[196],"Ansatz":[200,229],"model.":[209],"This":[210,285],"us":[212],"describe":[214],"part":[216,246],"does":[232],"not":[233],"collapse":[234],"zero":[236],"Within":[243],"considered":[245],"identify":[252],"dominant":[254],"show":[257],"those":[259],"correlations":[260],"lengths":[261],"diverge":[263],"given,":[269],"leading":[272],"order,":[273],"Boson":[280],"$c=1$":[281],"field":[283],"theory.":[284],"establishes":[287],"long-standing":[289],"conjecture":[290],"present":[291],"physics":[294],"literature.":[295]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2026-11-03T10:50:19.383937","created_date":"2023-10-13T00:00:00"}
