{"id":"https://openalex.org/W2003294699","doi":"https://doi.org/10.1103/physrevb.78.094404","title":"Class of exactly solvable S O ( n ) symmetric spin chains with matrix product ground states","display_name":"Class of exactly solvable S O ( n ) symmetric spin chains with matrix product ground states","publication_year":2008,"publication_date":"2008-09-08","ids":{"openalex":"https://openalex.org/W2003294699","doi":"https://doi.org/10.1103/physrevb.78.094404","mag":"2003294699"},"language":"lv","primary_location":{"id":"doi:10.1103/physrevb.78.094404","doi":"https://doi.org/10.1103/physrevb.78.094404","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrevb.78.094404","pdf_url":null,"source":{"id":"https://openalex.org/S6791298","display_name":"Physical Review B","issn_l":"1098-0121","issn":["1098-0121","1538-4489","1550-235X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review B","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0806.1839","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034664064","display_name":"Hong-Hao Tu","orcid":"https://orcid.org/0000-0003-0047-6087","observed_orcids":["https://orcid.org/0000-0003-0047-6087"]},"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":"Hong-Hao Tu","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":"middle","author":{"id":"https://openalex.org/A5100334992","display_name":"Guang-Ming Zhang","orcid":"https://orcid.org/0000-0002-9880-6023","observed_orcids":["https://orcid.org/0000-0002-9880-6023"]},"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":"Guang-Ming Zhang","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/A5043563677","display_name":"Tao Xiang","orcid":"https://orcid.org/0000-0001-5998-7338","observed_orcids":["https://orcid.org/0000-0001-5998-7338"]},"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":"Tao Xiang","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"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I99065089"],"apc_list":{"value":2675,"currency":"USD","value_usd":2675},"apc_paid":null,"fwci":5.0069,"has_fulltext":false,"cited_by_count":97,"citation_normalized_percentile":{"value":0.962519,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"78","issue":"9","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":0.8119999766349792,"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":0.8119999766349792,"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":0.18019999563694,"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/T10037","display_name":"Physics of Superconductivity and Magnetism","score":0.003100000089034438,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/exactly-solvable-hamiltonian","display_name":"exactly solvable Hamiltonian","score":0.8859999775886536},{"id":"https://openalex.org/keywords/haldane-gap","display_name":"Haldane gap","score":0.9559999704360962},{"id":"https://openalex.org/keywords/spin-liquid","display_name":"spin liquid","score":0.9120000004768372},{"id":"https://openalex.org/keywords/spontaneous-dimerization","display_name":"spontaneous dimerization","score":0.9010000228881836},{"id":"https://openalex.org/keywords/string-order-parameter","display_name":"string order parameter","score":0.8820000290870667},{"id":"https://openalex.org/keywords/bilinear-biquadratic-model","display_name":"bilinear-biquadratic model","score":0.925000011920929},{"id":"https://openalex.org/keywords/ground-state-phase-diagram","display_name":"ground-state phase diagram","score":0.8529999852180481},{"id":"https://openalex.org/keywords/translation-invariance","display_name":"translation invariance","score":0.8199999928474426}],"concepts":[{"id":"https://openalex.org/C69523127","wikidata":"https://www.wikidata.org/wiki/Q4480008","display_name":"Ground state","level":2,"score":0.6708369851112366},{"id":"https://openalex.org/C155355069","wikidata":"https://www.wikidata.org/wiki/Q575224","display_name":"Antiferromagnetism","level":2,"score":0.6150946021080017},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.5015571117401123},{"id":"https://openalex.org/C85906118","wikidata":"https://www.wikidata.org/wiki/Q186693","display_name":"Phase diagram","level":3,"score":0.4982733726501465},{"id":"https://openalex.org/C2778351468","wikidata":"https://www.wikidata.org/wiki/Q17149634","display_name":"Matrix product state","level":4,"score":0.48723164200782776},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4731292128562927},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.45327767729759216},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.43787020444869995},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.3238765597343445},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.31584662199020386},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.29896047711372375},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.24702703952789307},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.2460707724094391},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.20387312769889832},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.20062708854675293},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.1480329930782318},{"id":"https://openalex.org/C60644358","wikidata":"https://www.wikidata.org/wiki/Q128570","display_name":"Bioinformatics","level":1,"score":0.10434621572494507},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1103/physrevb.78.094404","doi":"https://doi.org/10.1103/physrevb.78.094404","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrevb.78.094404","pdf_url":null,"source":{"id":"https://openalex.org/S6791298","display_name":"Physical Review B","issn_l":"1098-0121","issn":["1098-0121","1538-4489","1550-235X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review B","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0806.1839","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0806.1839","pdf_url":"https://arxiv.org/pdf/0806.1839","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.0806.1839","doi":"https://doi.org/10.48550/arxiv.0806.1839","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.0806.1839","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":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0806.1839","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0806.1839","pdf_url":"https://arxiv.org/pdf/0806.1839","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":61,"referenced_works":["https://openalex.org/W1660717591","https://openalex.org/W1968757657","https://openalex.org/W1975635086","https://openalex.org/W1976467405","https://openalex.org/W1978765270","https://openalex.org/W1986289435","https://openalex.org/W1986315623","https://openalex.org/W1986726041","https://openalex.org/W1987817388","https://openalex.org/W1988836763","https://openalex.org/W1990681488","https://openalex.org/W1990885492","https://openalex.org/W1993787241","https://openalex.org/W1999354641","https://openalex.org/W1999764527","https://openalex.org/W2000034650","https://openalex.org/W2006574499","https://openalex.org/W2008017776","https://openalex.org/W2008317504","https://openalex.org/W2016291771","https://openalex.org/W2020123624","https://openalex.org/W2021044075","https://openalex.org/W2023643569","https://openalex.org/W2027639122","https://openalex.org/W2028656212","https://openalex.org/W2034042302","https://openalex.org/W2035382765","https://openalex.org/W2035781369","https://openalex.org/W2040059039","https://openalex.org/W2041156691","https://openalex.org/W2051927072","https://openalex.org/W2051952375","https://openalex.org/W2055233086","https://openalex.org/W2056258374","https://openalex.org/W2059292006","https://openalex.org/W2068918752","https://openalex.org/W2073778876","https://openalex.org/W2075677506","https://openalex.org/W2076904838","https://openalex.org/W2077661384","https://openalex.org/W2081240187","https://openalex.org/W2081997003","https://openalex.org/W2082114101","https://openalex.org/W2083202559","https://openalex.org/W2084850372","https://openalex.org/W2085767401","https://openalex.org/W2085919414","https://openalex.org/W2087539368","https://openalex.org/W2087638084","https://openalex.org/W2088634359","https://openalex.org/W2091807125","https://openalex.org/W2113166233","https://openalex.org/W2123122881","https://openalex.org/W2146518949","https://openalex.org/W2151990752","https://openalex.org/W2159327943","https://openalex.org/W2161246334","https://openalex.org/W2230547431","https://openalex.org/W2317586084","https://openalex.org/W3144135507","https://openalex.org/W4235284319"],"related_works":["https://openalex.org/W1966373152","https://openalex.org/W1963659195","https://openalex.org/W2088758181","https://openalex.org/W2007775649","https://openalex.org/W2064176266","https://openalex.org/W1744990718","https://openalex.org/W1984055548","https://openalex.org/W7100451940","https://openalex.org/W2010699112","https://openalex.org/W3122608403"],"abstract_inverted_index":{"We":[0],"introduce":[1],"a":[2,24,42,60,77],"class":[3],"of":[4,76],"exactly":[5],"solvable":[6],"$SO(n)$":[7,79],"symmetric":[8,80],"Hamiltonians":[9],"with":[10,46],"matrix":[11,51],"product":[12,52],"ground":[13,21,39,53],"states.":[14],"For":[15],"an":[16,34],"odd":[17],"$n\\ensuremath{\\ge}3$":[18],"case,":[19,37],"the":[20,38,50],"state":[22,40,45],"is":[23,41,65,83],"translational":[25],"invariant":[26],"Haldane":[27],"gap":[28],"spin":[29],"liquid":[30],"state;":[31],"while":[32],"for":[33,55],"even":[35],"$n\\ensuremath{\\ge}4$":[36],"spontaneously":[43],"dimerized":[44],"twofold":[47],"degeneracy.":[48],"In":[49],"states":[54],"both":[56],"cases,":[57],"we":[58],"identify":[59],"hidden":[61],"antiferromagnetic":[62],"order,":[63],"which":[64],"characterized":[66],"by":[67],"nonlocal":[68],"string":[69],"order":[70],"parameters.":[71],"The":[72],"ground-state":[73],"phase":[74],"diagram":[75],"generalized":[78],"bilinear-biquadratic":[81],"model":[82],"discussed.":[84]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":9}],"updated_date":"2026-11-03T10:50:19.383937","created_date":"2016-06-24T00:00:00"}