{"id":"https://openalex.org/W4406692398","doi":"https://doi.org/10.1103/1qyd-59z7","title":"Parent Lindbladians for matrix product density operators","display_name":"Parent Lindbladians for matrix product density operators","publication_year":2026,"publication_date":"2026-01-15","ids":{"openalex":"https://openalex.org/W4406692398","doi":"https://doi.org/10.1103/1qyd-59z7"},"language":"en","primary_location":{"id":"doi:10.1103/1qyd-59z7","doi":"https://doi.org/10.1103/1qyd-59z7","is_oa":true,"landing_page_url":"https://doi.org/10.1103/1qyd-59z7","pdf_url":null,"source":{"id":"https://openalex.org/S4210240247","display_name":"Physical Review Research","issn_l":"2643-1564","issn":["2643-1564"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-b","jufo-1","norway-1","oarl","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review Research","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1103/1qyd-59z7","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100350533","display_name":"Yuhan Liu","orcid":"https://orcid.org/0000-0003-4201-7575","observed_orcids":["https://orcid.org/0000-0003-4201-7575"]},"institutions":[{"id":"https://openalex.org/I4210120293","display_name":"Max Planck Institute of Quantum Optics","ror":"https://ror.org/01vekys64","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210120293"]},{"id":"https://openalex.org/I4210142743","display_name":"Munich Center for Quantum Science and Technology","ror":"https://ror.org/04xrcta15","country_code":"DE","type":"education","lineage":["https://openalex.org/I4210142743","https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Yuhan Liu","raw_affiliation_strings":["Max Planck Institute of Quantum Optics","Munich Center for Quantum Science and Technology (MCQST)"],"raw_orcid":"https://orcid.org/0000-0003-4201-7575","affiliations":[{"raw_affiliation_string":"Max Planck Institute of Quantum Optics","institution_ids":["https://openalex.org/I4210120293"]},{"raw_affiliation_string":"Munich Center for Quantum Science and Technology (MCQST)","institution_ids":["https://openalex.org/I4210142743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025194175","display_name":"Alberto Ruiz-de-Alarc\u00f3n","orcid":"https://orcid.org/0000-0001-5726-2114","observed_orcids":["https://orcid.org/0000-0001-5726-2114"]},"institutions":[{"id":"https://openalex.org/I121748325","display_name":"Universidad Complutense de Madrid","ror":"https://ror.org/02p0gd045","country_code":"ES","type":"education","lineage":["https://openalex.org/I121748325"]},{"id":"https://openalex.org/I4403386682","display_name":"CUNEF Universidad","ror":"https://ror.org/02web8j86","country_code":"ES","type":"education","lineage":["https://openalex.org/I4403386682"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Alberto Ruiz-de-Alarc\u00f3n","raw_affiliation_strings":["CUNEF Universidad","Universidad Complutense de Madrid"],"raw_orcid":"https://orcid.org/0000-0001-5726-2114","affiliations":[{"raw_affiliation_string":"CUNEF Universidad","institution_ids":["https://openalex.org/I4403386682"]},{"raw_affiliation_string":"Universidad Complutense de Madrid","institution_ids":["https://openalex.org/I121748325"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079532037","display_name":"Georgios Styliaris","orcid":"https://orcid.org/0000-0002-6809-8505","observed_orcids":["https://orcid.org/0000-0002-6809-8505"]},"institutions":[{"id":"https://openalex.org/I4210120293","display_name":"Max Planck Institute of Quantum Optics","ror":"https://ror.org/01vekys64","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210120293"]},{"id":"https://openalex.org/I4210142743","display_name":"Munich Center for Quantum Science and Technology","ror":"https://ror.org/04xrcta15","country_code":"DE","type":"education","lineage":["https://openalex.org/I4210142743","https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Georgios Styliaris","raw_affiliation_strings":["Max Planck Institute of Quantum Optics","Munich Center for Quantum Science and Technology (MCQST)"],"raw_orcid":"https://orcid.org/0000-0002-6809-8505","affiliations":[{"raw_affiliation_string":"Max Planck Institute of Quantum Optics","institution_ids":["https://openalex.org/I4210120293"]},{"raw_affiliation_string":"Munich Center for Quantum Science and Technology (MCQST)","institution_ids":["https://openalex.org/I4210142743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000966743","display_name":"Xiao-Qi Sun","orcid":"https://orcid.org/0000-0002-5179-5187","observed_orcids":["https://orcid.org/0000-0002-5179-5187"]},"institutions":[{"id":"https://openalex.org/I4210120293","display_name":"Max Planck Institute of Quantum Optics","ror":"https://ror.org/01vekys64","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210120293"]},{"id":"https://openalex.org/I4210142743","display_name":"Munich Center for Quantum Science and Technology","ror":"https://ror.org/04xrcta15","country_code":"DE","type":"education","lineage":["https://openalex.org/I4210142743","https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Xiao-Qi Sun","raw_affiliation_strings":["Max Planck Institute of Quantum Optics","Munich Center for Quantum Science and Technology (MCQST)"],"raw_orcid":"https://orcid.org/0000-0002-5179-5187","affiliations":[{"raw_affiliation_string":"Max Planck Institute of Quantum Optics","institution_ids":["https://openalex.org/I4210120293"]},{"raw_affiliation_string":"Munich Center for Quantum Science and Technology (MCQST)","institution_ids":["https://openalex.org/I4210142743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037099975","display_name":"David P\u00e9rez-Garc\u0131\u0301a","orcid":"https://orcid.org/0000-0003-2990-791X","observed_orcids":["https://orcid.org/0000-0003-2990-791X"]},"institutions":[{"id":"https://openalex.org/I121748325","display_name":"Universidad Complutense de Madrid","ror":"https://ror.org/02p0gd045","country_code":"ES","type":"education","lineage":["https://openalex.org/I121748325"]},{"id":"https://openalex.org/I4210157032","display_name":"Institute of Mathematical Sciences","ror":"https://ror.org/05e9bn444","country_code":"ES","type":"facility","lineage":["https://openalex.org/I4210157032"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"David P\u00e9rez-Garc\u00eda","raw_affiliation_strings":["Instituto de Ciencias Matem\u00e1ticas","Universidad Complutense de Madrid"],"raw_orcid":"https://orcid.org/0000-0003-2990-791X","affiliations":[{"raw_affiliation_string":"Instituto de Ciencias Matem\u00e1ticas","institution_ids":["https://openalex.org/I4210157032"]},{"raw_affiliation_string":"Universidad Complutense de Madrid","institution_ids":["https://openalex.org/I121748325"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083228566","display_name":"J. I. Cirac","orcid":"https://orcid.org/0000-0003-3359-1743","observed_orcids":["https://orcid.org/0000-0003-3359-1743"]},"institutions":[{"id":"https://openalex.org/I4210120293","display_name":"Max Planck Institute of Quantum Optics","ror":"https://ror.org/01vekys64","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210120293"]},{"id":"https://openalex.org/I4210142743","display_name":"Munich Center for Quantum Science and Technology","ror":"https://ror.org/04xrcta15","country_code":"DE","type":"education","lineage":["https://openalex.org/I4210142743","https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"J. Ignacio Cirac","raw_affiliation_strings":["Max Planck Institute of Quantum Optics","Munich Center for Quantum Science and Technology (MCQST)"],"raw_orcid":"https://orcid.org/0000-0003-3359-1743","affiliations":[{"raw_affiliation_string":"Max Planck Institute of Quantum Optics","institution_ids":["https://openalex.org/I4210120293"]},{"raw_affiliation_string":"Munich Center for Quantum Science and Technology (MCQST)","institution_ids":["https://openalex.org/I4210142743"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2625,"currency":"USD","value_usd":2625},"apc_paid":{"value":2625,"currency":"USD","value_usd":2625},"fwci":7.7618,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.96216788,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"8","issue":"1","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":0.9990000128746033,"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":0.9990000128746033,"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":9.999999747378752e-05,"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/T10657","display_name":"Topological Materials and Phenomena","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/renormalization-fixed-point","display_name":"renormalization fixed point","score":0.9580000042915344},{"id":"https://openalex.org/keywords/steady-state","display_name":"steady state","score":0.7950000166893005},{"id":"https://openalex.org/keywords/topological-phases","display_name":"topological phases","score":0.7099999785423279},{"id":"https://openalex.org/keywords/one-dimensional-quantum-systems","display_name":"one-dimensional quantum systems","score":0.6710000038146973},{"id":"https://openalex.org/keywords/tensor-networks","display_name":"tensor networks","score":0.656000018119812}],"concepts":[{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5135831832885742},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5078149437904358},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.3325648307800293},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31968778371810913},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.15643912553787231},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05808338522911072},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0550273060798645}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1103/1qyd-59z7","doi":"https://doi.org/10.1103/1qyd-59z7","is_oa":true,"landing_page_url":"https://doi.org/10.1103/1qyd-59z7","pdf_url":null,"source":{"id":"https://openalex.org/S4210240247","display_name":"Physical Review Research","issn_l":"2643-1564","issn":["2643-1564"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-b","jufo-1","norway-1","oarl","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review Research","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2501.10552","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2501.10552","pdf_url":"https://arxiv.org/pdf/2501.10552","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:85010b7076cb48cc981a2f6fd3842d5a","doi":null,"is_oa":false,"landing_page_url":"https://doaj.org/article/85010b7076cb48cc981a2f6fd3842d5a","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Physical Review Research, Vol 8, Iss 1, p 013210 (2026)","raw_type":"article"},{"id":"doi:10.48550/arxiv.2501.10552","doi":"https://doi.org/10.48550/arxiv.2501.10552","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2501.10552","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:10.1103/1qyd-59z7","doi":"https://doi.org/10.1103/1qyd-59z7","is_oa":true,"landing_page_url":"https://doi.org/10.1103/1qyd-59z7","pdf_url":null,"source":{"id":"https://openalex.org/S4210240247","display_name":"Physical Review Research","issn_l":"2643-1564","issn":["2643-1564"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-b","jufo-1","norway-1","oarl","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review Research","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1175115578","display_name":null,"funder_award_id":"AEI//10.13039/501100011033/","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G121809054","display_name":null,"funder_award_id":"MCIN/AEI/10","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G1768993395","display_name":null,"funder_award_id":"EXC 2111","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G1855990336","display_name":null,"funder_award_id":".13039/501100011033","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G1908868068","display_name":null,"funder_award_id":"CEX2023\u2010001347\u2010S","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G210041235","display_name":null,"funder_award_id":"MCIN /AEI/ 10.13039/501100011033","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G2262748287","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G2309174360","display_name":null,"funder_award_id":"10.13039","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G2601397997","display_name":null,"funder_award_id":"10.13039/501100011033","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G2660406951","display_name":null,"funder_award_id":"/ AEI/10","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G2756433129","display_name":null,"funder_award_id":"MCIN /AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G279363373","display_name":null,"funder_award_id":"MCIN/AEI/10.13039/501100011033,","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G2960115771","display_name":null,"funder_award_id":"390814868","funder_id":"https://openalex.org/F4320331500","funder_display_name":"Munich Center for Quantum Science and Technology"},{"id":"https://openalex.org/G300979063","display_name":null,"funder_award_id":"10.13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G34346518","display_name":null,"funder_award_id":"MCIN/AEI/10.13039/501 100 011 033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3480869486","display_name":null,"funder_award_id":"13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3681454997","display_name":null,"funder_award_id":"13039/501100011033","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G379951279","display_name":null,"funder_award_id":"FEI-EU-22-06","funder_id":"https://openalex.org/F4320321585","funder_display_name":"Universidad Complutense de Madrid"},{"id":"https://openalex.org/G4042783231","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G4192779913","display_name":null,"funder_award_id":"TEC-2024/COM-84-QUITEMAD- CM","funder_id":"https://openalex.org/F4320313831","funder_display_name":"Comunidad de Madrid"},{"id":"https://openalex.org/G425668148","display_name":null,"funder_award_id":".13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G430777504","display_name":null,"funder_award_id":"10.13039/501100011033/","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G455862292","display_name":null,"funder_award_id":"CEX2023- 001347-S","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G4710139657","display_name":null,"funder_award_id":"EXC- 2111390814868","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G4886082077","display_name":null,"funder_award_id":"PID2020-113523GB-I00","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G5080475149","display_name":null,"funder_award_id":"10.13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G5195188938","display_name":null,"funder_award_id":"/AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5421974903","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G5768859344","display_name":null,"funder_award_id":"EXC-2111","funder_id":"https://openalex.org/F4320331500","funder_display_name":"Munich Center for Quantum Science and Technology"},{"id":"https://openalex.org/G5805502524","display_name":null,"funder_award_id":"PID2020","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G7084143925","display_name":null,"funder_award_id":"AEI/10","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G712370837","display_name":null,"funder_award_id":"PID2020\u2013113523 GB-I00","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G866891011","display_name":null,"funder_award_id":"EXC 2111\u2013390814868","funder_id":"https://openalex.org/F4320331500","funder_display_name":"Munich Center for Quantum Science and Technology"},{"id":"https://openalex.org/G8709851231","display_name":"EXC 2111: Munich Center for Quantum Science and Technology (MCQST)","funder_award_id":"390814868","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G897484643","display_name":null,"funder_award_id":"MCIN /AEI /10.13039","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G99296377","display_name":null,"funder_award_id":"/AEI/10.13039/ 501100011033","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320308269","display_name":"Alexander von Humboldt-Stiftung","ror":"https://ror.org/012kf4317"},{"id":"https://openalex.org/F4320313831","display_name":"Comunidad de Madrid","ror":null},{"id":"https://openalex.org/F4320319880","display_name":"Government of Canada","ror":"https://ror.org/010q4q527"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321114","display_name":"Bundesministerium f\u00fcr Bildung und Forschung","ror":"https://ror.org/04pz7b180"},{"id":"https://openalex.org/F4320321585","display_name":"Universidad Complutense de Madrid","ror":"https://ror.org/02p0gd045"},{"id":"https://openalex.org/F4320322930","display_name":"Ministerio de Ciencia e Innovaci\u00f3n","ror":null},{"id":"https://openalex.org/F4320331462","display_name":"Institut P\u00e9rim\u00e8tre de physique th\u00e9orique","ror":"https://ror.org/013m0ej23"},{"id":"https://openalex.org/F4320331473","display_name":"Ministry of Colleges and Universities","ror":null},{"id":"https://openalex.org/F4320331500","display_name":"Munich Center for Quantum Science and Technology","ror":"https://ror.org/04xrcta15"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":"https://ror.org/003x0zc53"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W1565141348","https://openalex.org/W1579013843","https://openalex.org/W1678198585","https://openalex.org/W1852157478","https://openalex.org/W1860740507","https://openalex.org/W1892476723","https://openalex.org/W1942206397","https://openalex.org/W1969631049","https://openalex.org/W1977658351","https://openalex.org/W2015683881","https://openalex.org/W2019024022","https://openalex.org/W2019692968","https://openalex.org/W2035573654","https://openalex.org/W2041461270","https://openalex.org/W2057368709","https://openalex.org/W2061649613","https://openalex.org/W2062476673","https://openalex.org/W2071849960","https://openalex.org/W2072296482","https://openalex.org/W2073938011","https://openalex.org/W2074426935","https://openalex.org/W2077454431","https://openalex.org/W2077485894","https://openalex.org/W2084642564","https://openalex.org/W2099265531","https://openalex.org/W2099773315","https://openalex.org/W2105077826","https://openalex.org/W2112057469","https://openalex.org/W2122816100","https://openalex.org/W2173452581","https://openalex.org/W2197788506","https://openalex.org/W2408773496","https://openalex.org/W2895838543","https://openalex.org/W2950005313","https://openalex.org/W4200400528","https://openalex.org/W4226271997","https://openalex.org/W4385707242","https://openalex.org/W4392763773","https://openalex.org/W4394657114","https://openalex.org/W4402410224","https://openalex.org/W4402861860","https://openalex.org/W4403748992","https://openalex.org/W4404038478","https://openalex.org/W4406661666","https://openalex.org/W4406662082","https://openalex.org/W4406758293","https://openalex.org/W4406915829","https://openalex.org/W4408015984","https://openalex.org/W4408189470","https://openalex.org/W4408302779","https://openalex.org/W4408661598","https://openalex.org/W4408788422","https://openalex.org/W4408798448","https://openalex.org/W4410550711","https://openalex.org/W4417178184"],"related_works":["https://openalex.org/W3210622355","https://openalex.org/W7172525953","https://openalex.org/W3094960262","https://openalex.org/W4404342611","https://openalex.org/W2895838543","https://openalex.org/W4224330894","https://openalex.org/W3013002783","https://openalex.org/W7213500158","https://openalex.org/W2734489424","https://openalex.org/W4404050184"],"abstract_inverted_index":{"Understanding":[0],"quantum":[1],"phases":[2,17,61,70],"of":[3,16,22,62,84,93,115,171],"matter":[4,63],"is":[5],"a":[6,151,185],"fundamental":[7],"goal":[8],"in":[9,64,88],"physics.":[10],"For":[11],"pure":[12],"states,":[13,47,86],"the":[14,19,81,90,94,169,172,176,179],"representatives":[15],"are":[18,27,36,54,56,135],"ground":[20],"states":[21,35,114],"locally":[23],"interacting":[24],"Hamiltonians,":[25],"which":[26],"also":[28],"renormalization":[29],"fixed":[30],"points":[31],"(RFPs).":[32],"These":[33,133],"RFP":[34,182],"exactly":[37],"described":[38],"by":[39,125],"tensor":[40],"networks.":[41],"Extending":[42],"this":[43,119,123],"framework":[44],"to":[45,58,75,78,184],"mixed":[46],"matrix":[48],"product":[49],"density":[50],"operators":[51],"(MPDOs)":[52],"that":[53,147,154,178],"RFPs":[55,108],"believed":[57],"encapsulate":[59],"mixed-state":[60],"one":[65],"dimension,":[66],"where":[67],"nontrivial":[68,186],"topological":[69],"have":[71],"already":[72],"been":[73],"shown":[74],"exist.":[76],"However,":[77],"better":[79],"motivate":[80],"physical":[82,91],"relevance":[83,92],"those":[85],"and":[87,139,175],"particular":[89],"recently":[95],"found":[96],"non":[97],"trivial":[98],"phases,":[99],"it":[100],"remains":[101],"an":[102,165],"open":[103],"question":[104,124],"whether":[105],"such":[106],"MPDO":[107,131,181],"can":[109],"be":[110],"realized":[111],"as":[112],"steady":[113],"local":[116],"Lindbladians.":[117],"In":[118,161],"work,":[120],"we":[121,145,163],"resolve":[122],"analytically":[126],"constructing":[127],"parent":[128,148],"Lindbladians":[129,134,149],"for":[130],"RFPs.":[132],"local,":[136],"frustration":[137],"free,":[138],"exhibit":[140],"minimal":[141],"steady-state":[142],"degeneracy.":[143],"Interestingly,":[144],"find":[146],"possess":[150],"rich":[152],"structure":[153],"distinguishes":[155],"them":[156],"from":[157],"their":[158],"Hamiltonian":[159],"counterparts.":[160],"particular,":[162],"uncover":[164],"intriguing":[166],"connection":[167],"between":[168],"noncommutativity":[170],"Lindbladian":[173],"terms":[174],"fact":[177],"corresponding":[180],"belongs":[183],"phase.":[187]},"counts_by_year":[{"year":2026,"cited_by_count":3}],"updated_date":"2026-10-27T15:51:10.671819","created_date":"2025-01-23T00:00:00"}
