{"id":"https://openalex.org/W2969503693","doi":"https://doi.org/10.3390/e21090836","title":"Scaling of the Berry Phase in the Yang-Lee Edge Singularity","display_name":"Scaling of the Berry Phase in the Yang-Lee Edge Singularity","publication_year":2019,"publication_date":"2019-08-26","ids":{"openalex":"https://openalex.org/W2969503693","doi":"https://doi.org/10.3390/e21090836","mag":"2969503693"},"language":"en","primary_location":{"id":"doi:10.3390/e21090836","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21090836","pdf_url":"https://www.mdpi.com/1099-4300/21/9/836/pdf?version=1566811022","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/21/9/836/pdf?version=1566811022","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101482590","display_name":"Liang-Jun Zhai","orcid":"https://orcid.org/0000-0003-4483-689X"},"institutions":[{"id":"https://openalex.org/I4210144214","display_name":"Jiangsu University of Technology","ror":"https://ror.org/04jabhf80","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210144214"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liang-Jun Zhai","raw_affiliation_strings":["The School of Mathematics and Physics, Jiangsu University of Technology, Changzhou 213001, China"],"raw_orcid":"https://orcid.org/0000-0003-4483-689X","affiliations":[{"raw_affiliation_string":"The School of Mathematics and Physics, Jiangsu University of Technology, Changzhou 213001, China","institution_ids":["https://openalex.org/I4210144214"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100706684","display_name":"Huai\u2010Yu Wang","orcid":"https://orcid.org/0000-0001-9107-6120"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huai-Yu Wang","raw_affiliation_strings":["Department of Physics, Tsinghua University, Beijing 100084, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Tsinghua University, Beijing 100084, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083679603","display_name":"Guang-Yao Huang","orcid":"https://orcid.org/0000-0002-1073-9226"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Guang-Yao Huang","raw_affiliation_strings":["Institute for Quantum Information &amp; State Key Laboratory of High Performance Computing, College of Computer, National University of Defense Technology, Changsha 410073, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Quantum Information &amp; State Key Laboratory of High Performance Computing, College of Computer, National University of Defense Technology, Changsha 410073, China","institution_ids":["https://openalex.org/I170215575"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5083679603"],"corresponding_institution_ids":["https://openalex.org/I170215575"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.3004,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.61014627,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"21","issue":"9","first_page":"836","last_page":"836"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.9998999834060669,"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/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.9998999834060669,"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/T10657","display_name":"Topological Materials and Phenomena","score":0.9987000226974487,"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":0.9965000152587891,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/berry-connection-and-curvature","display_name":"Berry connection and curvature","score":0.6839424967765808},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.6685538291931152},{"id":"https://openalex.org/keywords/quantum-phase-transition","display_name":"Quantum phase transition","score":0.6541171073913574},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.6479130983352661},{"id":"https://openalex.org/keywords/phase-transition","display_name":"Phase transition","score":0.6346275806427002},{"id":"https://openalex.org/keywords/geometric-phase","display_name":"Geometric phase","score":0.6141741275787354},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.6000890135765076},{"id":"https://openalex.org/keywords/ising-model","display_name":"Ising model","score":0.599681556224823},{"id":"https://openalex.org/keywords/critical-exponent","display_name":"Critical exponent","score":0.5959904789924622},{"id":"https://openalex.org/keywords/dissipative-system","display_name":"Dissipative system","score":0.542264461517334},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.4964028000831604},{"id":"https://openalex.org/keywords/quantum-critical-point","display_name":"Quantum critical point","score":0.4745695888996124},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.4666077494621277},{"id":"https://openalex.org/keywords/critical-phenomena","display_name":"Critical phenomena","score":0.44579342007637024},{"id":"https://openalex.org/keywords/imaginary-time","display_name":"Imaginary time","score":0.41035863757133484},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.404867947101593},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.37559956312179565},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.37254199385643005},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.1930277943611145},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11566519737243652},{"id":"https://openalex.org/keywords/quantum-dynamics","display_name":"Quantum dynamics","score":0.09426933526992798}],"concepts":[{"id":"https://openalex.org/C22448393","wikidata":"https://www.wikidata.org/wiki/Q4894840","display_name":"Berry connection and curvature","level":3,"score":0.6839424967765808},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.6685538291931152},{"id":"https://openalex.org/C72190298","wikidata":"https://www.wikidata.org/wiki/Q2118253","display_name":"Quantum phase transition","level":3,"score":0.6541171073913574},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.6479130983352661},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.6346275806427002},{"id":"https://openalex.org/C17269025","wikidata":"https://www.wikidata.org/wiki/Q3283","display_name":"Geometric phase","level":2,"score":0.6141741275787354},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6000890135765076},{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.599681556224823},{"id":"https://openalex.org/C164154869","wikidata":"https://www.wikidata.org/wiki/Q901927","display_name":"Critical exponent","level":3,"score":0.5959904789924622},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.542264461517334},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.4964028000831604},{"id":"https://openalex.org/C146366752","wikidata":"https://www.wikidata.org/wiki/Q7269030","display_name":"Quantum critical point","level":4,"score":0.4745695888996124},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.4666077494621277},{"id":"https://openalex.org/C194807282","wikidata":"https://www.wikidata.org/wiki/Q900634","display_name":"Critical phenomena","level":3,"score":0.44579342007637024},{"id":"https://openalex.org/C88850056","wikidata":"https://www.wikidata.org/wiki/Q3274262","display_name":"Imaginary time","level":5,"score":0.41035863757133484},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.404867947101593},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.37559956312179565},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.37254199385643005},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1930277943611145},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11566519737243652},{"id":"https://openalex.org/C15184713","wikidata":"https://www.wikidata.org/wiki/Q7269042","display_name":"Quantum dynamics","level":3,"score":0.09426933526992798},{"id":"https://openalex.org/C177414767","wikidata":"https://www.wikidata.org/wiki/Q587607","display_name":"Supersymmetric quantum mechanics","level":4,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e21090836","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21090836","pdf_url":"https://www.mdpi.com/1099-4300/21/9/836/pdf?version=1566811022","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:84d7742e7b5b47b5ae791f9272f352d7","is_oa":true,"landing_page_url":"https://doaj.org/article/84d7742e7b5b47b5ae791f9272f352d7","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,"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":"Entropy, Vol 21, Iss 9, p 836 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/21/9/836/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e21090836","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7515365","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7515365","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e21090836","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21090836","pdf_url":"https://www.mdpi.com/1099-4300/21/9/836/pdf?version=1566811022","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8627812235","display_name":null,"funder_award_id":"11704161 and  11547142","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":62,"referenced_works":["https://openalex.org/W326669990","https://openalex.org/W1622764420","https://openalex.org/W1649271673","https://openalex.org/W1903186091","https://openalex.org/W1967226033","https://openalex.org/W1976576522","https://openalex.org/W1982882685","https://openalex.org/W1987585247","https://openalex.org/W1992904130","https://openalex.org/W1994748598","https://openalex.org/W1995139978","https://openalex.org/W1995791433","https://openalex.org/W1997323544","https://openalex.org/W1997983196","https://openalex.org/W2001821737","https://openalex.org/W2009768419","https://openalex.org/W2018600432","https://openalex.org/W2020459381","https://openalex.org/W2026874284","https://openalex.org/W2030667199","https://openalex.org/W2036523055","https://openalex.org/W2039754145","https://openalex.org/W2040036783","https://openalex.org/W2041433557","https://openalex.org/W2042612631","https://openalex.org/W2044489689","https://openalex.org/W2048503153","https://openalex.org/W2049850761","https://openalex.org/W2050924104","https://openalex.org/W2067123857","https://openalex.org/W2080095588","https://openalex.org/W2086031744","https://openalex.org/W2089005763","https://openalex.org/W2090911654","https://openalex.org/W2095019046","https://openalex.org/W2097780038","https://openalex.org/W2128224603","https://openalex.org/W2132568564","https://openalex.org/W2151895170","https://openalex.org/W2157723930","https://openalex.org/W2159837449","https://openalex.org/W2227075066","https://openalex.org/W2237612148","https://openalex.org/W2522470739","https://openalex.org/W2526518998","https://openalex.org/W2588008012","https://openalex.org/W2739884744","https://openalex.org/W2751877721","https://openalex.org/W2778618666","https://openalex.org/W2781491230","https://openalex.org/W2788022603","https://openalex.org/W3101229002","https://openalex.org/W3101946929","https://openalex.org/W3101999675","https://openalex.org/W3104472445","https://openalex.org/W3104668646","https://openalex.org/W3174658623","https://openalex.org/W4239702435","https://openalex.org/W4253292144","https://openalex.org/W4308326495","https://openalex.org/W6674952435","https://openalex.org/W6748378401"],"related_works":["https://openalex.org/W2419268402","https://openalex.org/W2164806646","https://openalex.org/W2240753919","https://openalex.org/W4297983310","https://openalex.org/W3007242136","https://openalex.org/W3132892312","https://openalex.org/W2396033766","https://openalex.org/W2975720390","https://openalex.org/W2020175698","https://openalex.org/W3115424227"],"abstract_inverted_index":{"We":[0,59],"study":[1],"the":[2,6,10,16,23,38,52,57,62,68,75,81,87,103,109,117,133,146,149,153,157],"scaling":[3,127],"behavior":[4,151],"of":[5,15,67,78,108,148],"Berry":[7,70,110,135],"phase":[8,40,48,71,97,111,136,154],"in":[9,28,156],"Yang-Lee":[11],"edge":[12],"singularity":[13],"(YLES)":[14],"non-Hermitian":[17,158],"quantum":[18,25],"system.":[19],"A":[20],"representative":[21],"model,":[22,37],"one-dimensional":[24],"Ising":[26],"model":[27],"an":[29],"imaginary":[30,53,65,106],"longitudinal":[31],"field,":[32],"is":[33],"selected.":[34],"For":[35],"this":[36],"dissipative":[39],"transition":[41,98,155],"(DPT),":[42],"accompanying":[43],"a":[44,141],"parity-time":[45],"(PT)":[46],"symmetry-breaking":[47],"transition,":[49],"occurs":[50],"when":[51],"field":[54],"changes":[55],"through":[56],"YLES.":[58,79],"find":[60,101],"that":[61,102,132],"real":[63,104],"and":[64,92,105,122,152],"parts":[66,107],"complex":[69,134],"show":[72],"anomalies":[73],"around":[74],"critical":[76,83,150],"points":[77],"In":[80],"overlapping":[82],"regions":[84],"constituted":[85],"by":[86,115],"(0":[88,118],"+":[89,94,119,124],"1)D":[90,95,120,125],"YLES":[91,121],"(1":[93,123],"ferromagnetic-paramagnetic":[96],"(FPPT),":[99],"we":[100],"can":[112,137],"be":[113,138],"described":[114],"both":[116],"FPPT":[126],"theory.":[128],"Our":[129],"results":[130],"demonstrate":[131],"used":[139],"as":[140],"universal":[142],"order":[143],"parameter":[144],"for":[145],"description":[147],"systems.":[159]},"counts_by_year":[{"year":2020,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
