{"id":"https://openalex.org/W7124821403","doi":null,"title":"Topological aspects of the gapless and the gapped","display_name":"Topological aspects of the gapless and the gapped","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W7124821403"},"language":"en","primary_location":{"id":"pmh:oai:dare.uva.nl:openaire_cris_publications/9d1a6e75-081b-486f-9cc6-f909cee71c1e","doi":null,"is_oa":true,"landing_page_url":"https://handle.uba.uva.nl/personal/pure/en/publications/topological-aspects-of-the-gapless-and-the-gapped(9d1a6e75-081b-486f-9cc6-f909cee71c1e).html","pdf_url":"https://pure.uva.nl/ws/files/193891232/Thesis.pdf","source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Vitouladitis, E 2024, 'Topological aspects of the gapless and the gapped', Doctor of Philosophy, Universiteit van Amsterdam.","raw_type":"info:eu-repo/semantics/other"},"volume":null,"type":"other","is_traditional":false,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://pure.uva.nl/ws/files/193891232/Thesis.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012217196","display_name":"Stathis Vitouladitis","orcid":"https://orcid.org/0000-0002-9641-4886","observed_orcids":["https://orcid.org/0000-0002-9641-4886"]},"institutions":[{"id":"https://openalex.org/I887064364","display_name":"University of Amsterdam","ror":"https://ror.org/04dkp9463","country_code":"NL","type":"education","lineage":["https://openalex.org/I887064364"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Vitouladitis, E.","raw_affiliation_strings":["aan de Universiteit van Amsterdam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"aan de Universiteit van Amsterdam","institution_ids":["https://openalex.org/I887064364"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5012217196"],"corresponding_institution_ids":["https://openalex.org/I887064364"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.6128000020980835,"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":0.6128000020980835,"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":0.1949000060558319,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.07800000160932541,"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/topological-order","display_name":"topological order","score":0.9330000281333923},{"id":"https://openalex.org/keywords/long-range-entanglement","display_name":"long-range entanglement","score":0.7519999742507935},{"id":"https://openalex.org/keywords/topological-quantum-field-theory","display_name":"topological field theory","score":0.8050000071525574},{"id":"https://openalex.org/keywords/topological-entanglement-entropy","display_name":"topological entanglement entropy","score":0.9850000143051147},{"id":"https://openalex.org/keywords/higher-form-symmetries","display_name":"higher-form symmetries","score":0.8539999723434448},{"id":"https://openalex.org/keywords/non-invertible-symmetries","display_name":"non-invertible symmetries","score":0.9290000200271606},{"id":"https://openalex.org/keywords/conformal-field-theory","display_name":"conformal field theory","score":0.8669999837875366},{"id":"https://openalex.org/keywords/edge-states","display_name":"edge states","score":0.5950000286102295},{"id":"https://openalex.org/keywords/line-operators","display_name":"line operators","score":0.8059999942779541},{"id":"https://openalex.org/keywords/gapped-phases","display_name":"gapped phases","score":0.5120000243186951},{"id":"https://openalex.org/keywords/gapless-phase","display_name":"gapless phase","score":0.8939999938011169},{"id":"https://openalex.org/keywords/topological-operators","display_name":"topological operators","score":0.3109999895095825}],"concepts":[{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.6905999779701233},{"id":"https://openalex.org/C148908050","wikidata":"https://www.wikidata.org/wiki/Q11681505","display_name":"Topological entropy in physics","level":3,"score":0.6891000270843506},{"id":"https://openalex.org/C7503960","wikidata":"https://www.wikidata.org/wiki/Q721094","display_name":"Topological quantum field theory","level":2,"score":0.6290000081062317},{"id":"https://openalex.org/C92542899","wikidata":"https://www.wikidata.org/wiki/Q7661340","display_name":"Symmetry protected topological order","level":4,"score":0.6080999970436096},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.5422000288963318},{"id":"https://openalex.org/C45646460","wikidata":"https://www.wikidata.org/wiki/Q17165159","display_name":"Topological order","level":3,"score":0.5174999833106995},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5116999745368958},{"id":"https://openalex.org/C24057170","wikidata":"https://www.wikidata.org/wiki/Q2497305","display_name":"Gapless playback","level":2,"score":0.5083000063896179},{"id":"https://openalex.org/C128911142","wikidata":"https://www.wikidata.org/wiki/Q1488689","display_name":"Topological insulator","level":2,"score":0.4383000135421753},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.427700012922287},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.39879998564720154},{"id":"https://openalex.org/C199793620","wikidata":"https://www.wikidata.org/wiki/Q7825030","display_name":"Topological degeneracy","level":5,"score":0.3970000147819519},{"id":"https://openalex.org/C115047598","wikidata":"https://www.wikidata.org/wiki/Q54505","display_name":"Quantum field theory","level":2,"score":0.387800008058548},{"id":"https://openalex.org/C54613284","wikidata":"https://www.wikidata.org/wiki/Q1191271","display_name":"Conformal field theory","level":3,"score":0.3695000112056732},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.3450999855995178},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.3407999873161316},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.34049999713897705},{"id":"https://openalex.org/C77223115","wikidata":"https://www.wikidata.org/wiki/Q634781","display_name":"Topological quantum number","level":2,"score":0.3391999900341034},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3246999979019165},{"id":"https://openalex.org/C80891386","wikidata":"https://www.wikidata.org/wiki/Q7269084","display_name":"Quantum phases","level":4,"score":0.32260000705718994},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.2752000093460083},{"id":"https://openalex.org/C527218924","wikidata":"https://www.wikidata.org/wiki/Q964053","display_name":"Topological algebra","level":3,"score":0.27399998903274536},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.2572999894618988}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:dare.uva.nl:openaire_cris_publications/9d1a6e75-081b-486f-9cc6-f909cee71c1e","doi":null,"is_oa":true,"landing_page_url":"https://handle.uba.uva.nl/personal/pure/en/publications/topological-aspects-of-the-gapless-and-the-gapped(9d1a6e75-081b-486f-9cc6-f909cee71c1e).html","pdf_url":"https://pure.uva.nl/ws/files/193891232/Thesis.pdf","source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Vitouladitis, E 2024, 'Topological aspects of the gapless and the gapped', Doctor of Philosophy, Universiteit van Amsterdam.","raw_type":"info:eu-repo/semantics/other"},{"id":"pmh:oai:dipot.ulb.ac.be:2013/401571","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/401571","pdf_url":null,"source":{"id":"https://openalex.org/S4306401063","display_name":"D\u00e9p\u00f4t institutionnel de l'Universit\u00e9 libre de Bruxelles (Universit\u00e9 Libre de Bruxelles)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I132053463","host_organization_name":"Universit\u00e9 Libre de Bruxelles","host_organization_lineage":["https://openalex.org/I132053463"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/doctoralThesis"}],"best_oa_location":{"id":"pmh:oai:dare.uva.nl:openaire_cris_publications/9d1a6e75-081b-486f-9cc6-f909cee71c1e","doi":null,"is_oa":true,"landing_page_url":"https://handle.uba.uva.nl/personal/pure/en/publications/topological-aspects-of-the-gapless-and-the-gapped(9d1a6e75-081b-486f-9cc6-f909cee71c1e).html","pdf_url":"https://pure.uva.nl/ws/files/193891232/Thesis.pdf","source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Vitouladitis, E 2024, 'Topological aspects of the gapless and the gapped', Doctor of Philosophy, Universiteit van Amsterdam.","raw_type":"info:eu-repo/semantics/other"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321008","display_name":"Universiteit van Amsterdam","ror":"https://ror.org/04dkp9463"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7124821403.pdf","grobid_xml":"https://content.openalex.org/works/W7124821403.grobid-xml"},"referenced_works_count":291,"referenced_works":["https://openalex.org/W31677808","https://openalex.org/W84515655","https://openalex.org/W272026006","https://openalex.org/W603256842","https://openalex.org/W1479704546","https://openalex.org/W1482581596","https://openalex.org/W1485420831","https://openalex.org/W1486912333","https://openalex.org/W1553977507","https://openalex.org/W1591512602","https://openalex.org/W1615248269","https://openalex.org/W1619894398","https://openalex.org/W1701600206","https://openalex.org/W1710401991","https://openalex.org/W1748447111","https://openalex.org/W1756636439","https://openalex.org/W1758503877","https://openalex.org/W1777799841","https://openalex.org/W1778149611","https://openalex.org/W1807973447","https://openalex.org/W1846387892","https://openalex.org/W1878258232","https://openalex.org/W1889142700","https://openalex.org/W1892605745","https://openalex.org/W1946703250","https://openalex.org/W1961690734","https://openalex.org/W1964419676","https://openalex.org/W1966111782","https://openalex.org/W1968598896","https://openalex.org/W1969477859","https://openalex.org/W1970919326","https://openalex.org/W1971718645","https://openalex.org/W1975327607","https://openalex.org/W1975533626","https://openalex.org/W1975635086","https://openalex.org/W1976341577","https://openalex.org/W1978680414","https://openalex.org/W1979044848","https://openalex.org/W1979072898","https://openalex.org/W1980592934","https://openalex.org/W1980601527","https://openalex.org/W1984955973","https://openalex.org/W1987429953","https://openalex.org/W1989382250","https://openalex.org/W1990736874","https://openalex.org/W1993289500","https://openalex.org/W1995809559","https://openalex.org/W1999396802","https://openalex.org/W2003095492","https://openalex.org/W2003513046","https://openalex.org/W2004707560","https://openalex.org/W2007185418","https://openalex.org/W2008317504","https://openalex.org/W2009795089","https://openalex.org/W2010905129","https://openalex.org/W2011600774","https://openalex.org/W2013421285","https://openalex.org/W2014855769","https://openalex.org/W2015264143","https://openalex.org/W2016866779","https://openalex.org/W2016986040","https://openalex.org/W2017677894","https://openalex.org/W2018192827","https://openalex.org/W2019024022","https://openalex.org/W2021029482","https://openalex.org/W2022544578","https://openalex.org/W2031170322","https://openalex.org/W2031521506","https://openalex.org/W2032761638","https://openalex.org/W2037673637","https://openalex.org/W2037833427","https://openalex.org/W2039843295","https://openalex.org/W2041537382","https://openalex.org/W2043746520","https://openalex.org/W2044657755","https://openalex.org/W2046439097","https://openalex.org/W2047906660","https://openalex.org/W2048983555","https://openalex.org/W2051055381","https://openalex.org/W2051591291","https://openalex.org/W2052339150","https://openalex.org/W2052810501","https://openalex.org/W2053391393","https://openalex.org/W2057916018","https://openalex.org/W2060647463","https://openalex.org/W2062009667","https://openalex.org/W2064100662","https://openalex.org/W2070712872","https://openalex.org/W2071333147","https://openalex.org/W2074507778","https://openalex.org/W2075253299","https://openalex.org/W2075852956","https://openalex.org/W2080447436","https://openalex.org/W2080580319","https://openalex.org/W2081301510","https://openalex.org/W2082257352","https://openalex.org/W2085541615","https://openalex.org/W2087405338","https://openalex.org/W2089254118","https://openalex.org/W2090466200","https://openalex.org/W2091894352","https://openalex.org/W2092760676","https://openalex.org/W2096271811","https://openalex.org/W2098411918","https://openalex.org/W2099017476","https://openalex.org/W2099710945","https://openalex.org/W2106578818","https://openalex.org/W2107240173","https://openalex.org/W2112842519","https://openalex.org/W2117449008","https://openalex.org/W2124948417","https://openalex.org/W2130445749","https://openalex.org/W2135486303","https://openalex.org/W2138487180","https://openalex.org/W2139101516","https://openalex.org/W2140746346","https://openalex.org/W2143935378","https://openalex.org/W2144480080","https://openalex.org/W2148705192","https://openalex.org/W2150045182","https://openalex.org/W2154971556","https://openalex.org/W2156682843","https://openalex.org/W2158891124","https://openalex.org/W2158923649","https://openalex.org/W2161021349","https://openalex.org/W2161091926","https://openalex.org/W2161239035","https://openalex.org/W2164929794","https://openalex.org/W2166429055","https://openalex.org/W2166879061","https://openalex.org/W2167976557","https://openalex.org/W2169919279","https://openalex.org/W2171135483","https://openalex.org/W2176355844","https://openalex.org/W2213712147","https://openalex.org/W2223420584","https://openalex.org/W2230547431","https://openalex.org/W2235517188","https://openalex.org/W2242924796","https://openalex.org/W2246296081","https://openalex.org/W2252601043","https://openalex.org/W2263651571","https://openalex.org/W2287712525","https://openalex.org/W2298547144","https://openalex.org/W2312216592","https://openalex.org/W2314766796","https://openalex.org/W2326825004","https://openalex.org/W2329262656","https://openalex.org/W2336209363","https://openalex.org/W2342176542","https://openalex.org/W2343647190","https://openalex.org/W2346228807","https://openalex.org/W2521499268","https://openalex.org/W2550343882","https://openalex.org/W2553497957","https://openalex.org/W2573798339","https://openalex.org/W2581933687","https://openalex.org/W2587122839","https://openalex.org/W2592119549","https://openalex.org/W2599432565","https://openalex.org/W2611893150","https://openalex.org/W2619077901","https://openalex.org/W2626052209","https://openalex.org/W2755611024","https://openalex.org/W2761379279","https://openalex.org/W2764000366","https://openalex.org/W2765573623","https://openalex.org/W2767188896","https://openalex.org/W2770212018","https://openalex.org/W2785656069","https://openalex.org/W2786370293","https://openalex.org/W2788013142","https://openalex.org/W2788815468","https://openalex.org/W2790814557","https://openalex.org/W2792784137","https://openalex.org/W2794132465","https://openalex.org/W2794912208","https://openalex.org/W2794966645","https://openalex.org/W2795268715","https://openalex.org/W2798232949","https://openalex.org/W2895920880","https://openalex.org/W2898066758","https://openalex.org/W2943934622","https://openalex.org/W2944927840","https://openalex.org/W2945426239","https://openalex.org/W2945496839","https://openalex.org/W2949530638","https://openalex.org/W2951623434","https://openalex.org/W2951935694","https://openalex.org/W2952605854","https://openalex.org/W2953044543","https://openalex.org/W2964270572","https://openalex.org/W2987777697","https://openalex.org/W2994467208","https://openalex.org/W2998882781","https://openalex.org/W3000268655","https://openalex.org/W3010871632","https://openalex.org/W3010983423","https://openalex.org/W3012099713","https://openalex.org/W3015263413","https://openalex.org/W3016259172","https://openalex.org/W3017207636","https://openalex.org/W3021613979","https://openalex.org/W3022633097","https://openalex.org/W3031301686","https://openalex.org/W3034826059","https://openalex.org/W3042062639","https://openalex.org/W3046137589","https://openalex.org/W3046218706","https://openalex.org/W3047694999","https://openalex.org/W3048635669","https://openalex.org/W3049733224","https://openalex.org/W3050554984","https://openalex.org/W3080588626","https://openalex.org/W3081626901","https://openalex.org/W3084070045","https://openalex.org/W3093891181","https://openalex.org/W3102870732","https://openalex.org/W3112417171","https://openalex.org/W3120837878","https://openalex.org/W3153302748","https://openalex.org/W3163419222","https://openalex.org/W3183520976","https://openalex.org/W3189816360","https://openalex.org/W3204128455","https://openalex.org/W3204923034","https://openalex.org/W3210489177","https://openalex.org/W3215790967","https://openalex.org/W3216198592","https://openalex.org/W3217405022","https://openalex.org/W4206688401","https://openalex.org/W4210597964","https://openalex.org/W4214812005","https://openalex.org/W4214950501","https://openalex.org/W4220745014","https://openalex.org/W4221162492","https://openalex.org/W4221162496","https://openalex.org/W4226120042","https://openalex.org/W4231217265","https://openalex.org/W4249956767","https://openalex.org/W4280586070","https://openalex.org/W4281264234","https://openalex.org/W4283360408","https://openalex.org/W4283700863","https://openalex.org/W4296022982","https://openalex.org/W4297383536","https://openalex.org/W4302014228","https://openalex.org/W4306952031","https://openalex.org/W4311515607","https://openalex.org/W4311639211","https://openalex.org/W4318151164","https://openalex.org/W4321089620","https://openalex.org/W4323543793","https://openalex.org/W4324130960","https://openalex.org/W4375869001","https://openalex.org/W4377099394","https://openalex.org/W4378347232","https://openalex.org/W4378900951","https://openalex.org/W4383369103","https://openalex.org/W4385959864","https://openalex.org/W4386925584","https://openalex.org/W4387796938","https://openalex.org/W4388181865","https://openalex.org/W4388596607","https://openalex.org/W4388910717","https://openalex.org/W4391708214","https://openalex.org/W4391988281","https://openalex.org/W4392122006","https://openalex.org/W4392425482","https://openalex.org/W4392593599","https://openalex.org/W4394663683","https://openalex.org/W4395071929","https://openalex.org/W4398770451","https://openalex.org/W4399098893","https://openalex.org/W4400197836","https://openalex.org/W4400387459","https://openalex.org/W4400788222","https://openalex.org/W4401887362","https://openalex.org/W4403032250","https://openalex.org/W4403656619","https://openalex.org/W4404162552","https://openalex.org/W4404163936","https://openalex.org/W4404481741","https://openalex.org/W4405367586","https://openalex.org/W4406761085","https://openalex.org/W4406800274","https://openalex.org/W4407028739","https://openalex.org/W4407073242","https://openalex.org/W4410373728","https://openalex.org/W4412656657","https://openalex.org/W7094039535"],"related_works":["https://openalex.org/W6990049910","https://openalex.org/W6948226624","https://openalex.org/W7107965672","https://openalex.org/W2945293867","https://openalex.org/W4391631984","https://openalex.org/W7047088825","https://openalex.org/W7164253864","https://openalex.org/W2611893150","https://openalex.org/W2177221036","https://openalex.org/W6982593648"],"abstract_inverted_index":{"Symmetry":[0],"is":[1,23,81,103,156,164,195,225],"a":[2,128,147,167,244,282],"fundamental":[3],"organising":[4],"principle":[5],"in":[6,39,61,269],"theoretical":[7],"physics,":[8,46],"underpinning":[9],"the":[10,16,41,124,171,192,196,210,213,248,277],"conservation":[11],"of":[12,18,20,44,66,113,120,130,141,150,170,174,198,247,251,271,297],"physical":[13],"quantities":[14],"and":[15,34,49,63,74,178,202,290,299],"characterisation":[17,246],"phases":[19,65],"matter.":[21],"It":[22,224],"closely":[24],"related":[25],"to":[26,29,57,145,158,181,206,235,281],"topology,":[27],"leading":[28],"generalisations":[30],"such":[31],"as":[32],"higher-form":[33,219],"non-invertible":[35],"symmetries,":[36,220],"with":[37,217,262,276],"applications":[38],"electromagnetism,":[40],"standard":[42],"model":[43],"particle":[45],"condensed":[47],"matter,":[48,67],"quantum":[50,97,107,249],"computation.":[51],"This":[52,163],"thesis":[53,115,214],"harnesses":[54],"generalised":[55],"symmetries":[56,265],"derive":[58],"universal":[59],"results":[60],"gapped":[62,86],"gapless":[64,211],"focusing":[68],"particularly":[69],"on":[70,117,287],"topologically":[71],"ordered":[72],"systems":[73],"conformal":[75],"field":[76,108],"theories":[77,109,253],"(CFTs).":[78],"Topological":[79],"order":[80],"characterised":[82],"by":[83,95,134,166],"long-range":[84,121],"entangled":[85],"phases,":[87],"namely":[88],"ground":[89],"states":[90,250,286],"that":[91,227],"cannot":[92],"be":[93,267],"disentangled":[94],"finite-depth":[96],"circuits.":[98],"At":[99],"low":[100],"energies":[101],"it":[102],"described":[104,133,237,268],"via":[105],"topological":[106,131,142,154,160],"(TQFTs).":[110],"One":[111],"part":[112],"this":[114,275],"focusses":[116],"extracting":[118],"patterns":[119],"entanglement":[122,161,182],"from":[123],"low-energy":[125],"TQFT":[126],"for":[127,243],"class":[129],"orders":[132],"abelian":[135,175],"BF":[136,176],"theory.":[137],"By":[138],"considering":[139],"algebras":[140,201,233],"operators":[143],"restricted":[144],"subregions,":[146],"new":[148],"measure":[149],"entanglement,":[151,155],"termed":[152],"essential":[153],"introduced":[157],"refine":[159],"entropy.":[162],"complemented":[165],"detailed":[168],"analysis":[169,279],"edge-mode":[172],"spectrum":[173],"theory":[177,205,241],"its":[179],"contribution":[180],"entropy":[183],"across":[184,254],"different":[185],"topologies.":[186,257],"A":[187],"key":[188],"mathematical":[189],"result,":[190],"enabling":[191],"above":[193],"analysis,":[194],"generalisation":[197],"Kac\u2013Moody":[199],"current":[200,232],"their":[203],"representation":[204,240],"higher":[207],"dimensions.":[208],"On":[209],"front,":[212],"considers":[215],"CFTs":[216,261],"continuous":[218,263],"invertible":[221],"or":[222],"non-invertible.":[223],"shown":[226],"they":[228],"also":[229],"possess":[230],"infinite-dimensional":[231],"akin":[234],"those":[236],"above.":[238],"Their":[239],"allows":[242],"complete":[245],"these":[252],"arbitrary":[255],"spatial":[256],"In":[258],"four":[259],"dimensions,":[260],"one-form":[264],"can":[266],"terms":[270],"free":[272],"photons.":[273],"Combining":[274],"previous":[278],"leads":[280],"one-to-one":[283],"correspondence":[284],"between":[285],"particular":[288],"topologies":[289],"line":[291],"operators,":[292],"i.e.":[293],"wires":[294],"carrying":[295],"distributions":[296],"electric":[298],"magnetic":[300],"charge.":[301]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-01-20T00:00:00"}