Subsystem non-invertible symmetry operators and defects Article Swipe
Weiguang Cao
,
Linhao Li
,
Masahito Yamazaki
,
Yunqin Zheng
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.21468/scipostphys.15.4.155
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.21468/scipostphys.15.4.155
We explore non-invertible symmetries in two-dimensional lattice models with subsystem \mathbb Z_2 symmetry. We introduce a subsystem \mathbb Z_2 -gauging procedure, called the subsystem Kramers-Wannier transformation, which generalizes the ordinary Kramers-Wannier transformation. The corresponding duality operators and defects are constructed by gaugings on the whole or half of the Hilbert space. By gauging twice, we derive fusion rules of duality operators and defects, which enriches ordinary Ising fusion rules with subsystem features. Subsystem Kramers-Wannier duality defects are mobile in both spatial directions, unlike the defects of invertible subsystem symmetries. We finally comment on the anomaly of the subsystem Kramers-Wannier duality symmetry, and discuss its subtleties.
Related Topics
Concepts
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.21468/scipostphys.15.4.155
- https://scipost.org/10.21468/SciPostPhys.15.4.155/pdf
- OA Status
- diamond
- Cited By
- 52
- References
- 237
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4366732312
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4366732312Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.21468/scipostphys.15.4.155Digital Object Identifier
- Title
-
Subsystem non-invertible symmetry operators and defectsWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2023Year of publication
- Publication date
-
2023-10-12Full publication date if available
- Authors
-
Weiguang Cao, Linhao Li, Masahito Yamazaki, Yunqin ZhengList of authors in order
- Landing page
-
https://doi.org/10.21468/scipostphys.15.4.155Publisher landing page
- PDF URL
-
https://scipost.org/10.21468/SciPostPhys.15.4.155/pdfDirect link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
diamondOpen access status per OpenAlex
- OA URL
-
https://scipost.org/10.21468/SciPostPhys.15.4.155/pdfDirect OA link when available
- Concepts
-
Invertible matrix, Symmetry (geometry), Mathematics, Theoretical physics, Pure mathematics, Physics, GeometryTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
52Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 23, 2024: 24, 2023: 5Per-year citation counts (last 5 years)
- References (count)
-
237Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W4366732312 |
|---|---|
| doi | https://doi.org/10.21468/scipostphys.15.4.155 |
| ids.doi | https://doi.org/10.21468/scipostphys.15.4.155 |
| ids.openalex | https://openalex.org/W4366732312 |
| fwci | 16.0659826 |
| type | article |
| title | Subsystem non-invertible symmetry operators and defects |
| awards[0].id | https://openalex.org/G6757501062 |
| awards[0].funder_id | https://openalex.org/F4320334764 |
| awards[0].display_name | |
| awards[0].funder_award_id | 23H01168 |
| awards[0].funder_display_name | Japan Society for the Promotion of Science |
| awards[1].id | https://openalex.org/G5877704734 |
| awards[1].funder_id | https://openalex.org/F4320334789 |
| awards[1].display_name | 誤り耐性型量子コンピュータにおける理論・ソフトウェアの研究開発 |
| awards[1].funder_award_id | JPMJMS2061 |
| awards[1].funder_display_name | Japan Science and Technology Agency |
| awards[2].id | https://openalex.org/G3826262035 |
| awards[2].funder_id | https://openalex.org/F4320334764 |
| awards[2].display_name | |
| awards[2].funder_award_id | 20H05860 |
| awards[2].funder_display_name | Japan Society for the Promotion of Science |
| awards[3].id | https://openalex.org/G2616774874 |
| awards[3].funder_id | https://openalex.org/F4320334764 |
| awards[3].display_name | |
| awards[3].funder_award_id | 19K03820 |
| awards[3].funder_display_name | Japan Society for the Promotion of Science |
| awards[4].id | https://openalex.org/G1322570085 |
| awards[4].funder_id | https://openalex.org/F4320334764 |
| awards[4].display_name | |
| awards[4].funder_award_id | JP22J21553 |
| awards[4].funder_display_name | Japan Society for the Promotion of Science |
| awards[5].id | https://openalex.org/G4553473049 |
| awards[5].funder_id | https://openalex.org/F4320334764 |
| awards[5].display_name | |
| awards[5].funder_award_id | JP19H05810 |
| awards[5].funder_display_name | Japan Society for the Promotion of Science |
| awards[6].id | https://openalex.org/G1453211129 |
| awards[6].funder_id | https://openalex.org/F4320334789 |
| awards[6].display_name | 固有状態熱化仮説の破れと場の理論の量子シミュレーション |
| awards[6].funder_award_id | JPMJPR225A |
| awards[6].funder_display_name | Japan Science and Technology Agency |
| awards[7].id | https://openalex.org/G5048732594 |
| awards[7].funder_id | https://openalex.org/F4320334764 |
| awards[7].display_name | |
| awards[7].funder_award_id | JP22KJ1072 |
| awards[7].funder_display_name | Japan Society for the Promotion of Science |
| awards[8].id | https://openalex.org/G3788267280 |
| awards[8].funder_id | https://openalex.org/F4320334764 |
| awards[8].display_name | |
| awards[8].funder_award_id | 19H00689 |
| awards[8].funder_display_name | Japan Society for the Promotion of Science |
| biblio.issue | 4 |
| biblio.volume | 15 |
| biblio.last_page | |
| biblio.first_page | |
| topics[0].id | https://openalex.org/T10792 |
| topics[0].field.id | https://openalex.org/fields/17 |
| topics[0].field.display_name | Computer Science |
| topics[0].score | 0.9983999729156494 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/1703 |
| topics[0].subfield.display_name | Computational Theory and Mathematics |
| topics[0].display_name | Matrix Theory and Algorithms |
| topics[1].id | https://openalex.org/T11022 |
| topics[1].field.id | https://openalex.org/fields/26 |
| topics[1].field.display_name | Mathematics |
| topics[1].score | 0.9973999857902527 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/2610 |
| topics[1].subfield.display_name | Mathematical Physics |
| topics[1].display_name | Spectral Theory in Mathematical Physics |
| topics[2].id | https://openalex.org/T10884 |
| topics[2].field.id | https://openalex.org/fields/26 |
| topics[2].field.display_name | Mathematics |
| topics[2].score | 0.9840999841690063 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/2604 |
| topics[2].subfield.display_name | Applied Mathematics |
| topics[2].display_name | Holomorphic and Operator Theory |
| funders[0].id | https://openalex.org/F4320320912 |
| funders[0].ror | https://ror.org/048rj2z13 |
| funders[0].display_name | Ministry of Education, Culture, Sports, Science and Technology |
| funders[1].id | https://openalex.org/F4320322832 |
| funders[1].ror | https://ror.org/057zh3y96 |
| funders[1].display_name | University of Tokyo |
| funders[2].id | https://openalex.org/F4320334764 |
| funders[2].ror | https://ror.org/00hhkn466 |
| funders[2].display_name | Japan Society for the Promotion of Science |
| funders[3].id | https://openalex.org/F4320334789 |
| funders[3].ror | https://ror.org/00097mb19 |
| funders[3].display_name | Japan Science and Technology Agency |
| is_xpac | False |
| apc_list | |
| apc_paid | |
| concepts[0].id | https://openalex.org/C96442724 |
| concepts[0].level | 2 |
| concepts[0].score | 0.8119981288909912 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q242188 |
| concepts[0].display_name | Invertible matrix |
| concepts[1].id | https://openalex.org/C2779886137 |
| concepts[1].level | 2 |
| concepts[1].score | 0.6937625408172607 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q21030012 |
| concepts[1].display_name | Symmetry (geometry) |
| concepts[2].id | https://openalex.org/C33923547 |
| concepts[2].level | 0 |
| concepts[2].score | 0.4542430639266968 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[2].display_name | Mathematics |
| concepts[3].id | https://openalex.org/C33332235 |
| concepts[3].level | 1 |
| concepts[3].score | 0.4339948296546936 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q18362 |
| concepts[3].display_name | Theoretical physics |
| concepts[4].id | https://openalex.org/C202444582 |
| concepts[4].level | 1 |
| concepts[4].score | 0.36487239599227905 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q837863 |
| concepts[4].display_name | Pure mathematics |
| concepts[5].id | https://openalex.org/C121332964 |
| concepts[5].level | 0 |
| concepts[5].score | 0.3507355749607086 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q413 |
| concepts[5].display_name | Physics |
| concepts[6].id | https://openalex.org/C2524010 |
| concepts[6].level | 1 |
| concepts[6].score | 0.12094458937644958 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q8087 |
| concepts[6].display_name | Geometry |
| keywords[0].id | https://openalex.org/keywords/invertible-matrix |
| keywords[0].score | 0.8119981288909912 |
| keywords[0].display_name | Invertible matrix |
| keywords[1].id | https://openalex.org/keywords/symmetry |
| keywords[1].score | 0.6937625408172607 |
| keywords[1].display_name | Symmetry (geometry) |
| keywords[2].id | https://openalex.org/keywords/mathematics |
| keywords[2].score | 0.4542430639266968 |
| keywords[2].display_name | Mathematics |
| keywords[3].id | https://openalex.org/keywords/theoretical-physics |
| keywords[3].score | 0.4339948296546936 |
| keywords[3].display_name | Theoretical physics |
| keywords[4].id | https://openalex.org/keywords/pure-mathematics |
| keywords[4].score | 0.36487239599227905 |
| keywords[4].display_name | Pure mathematics |
| keywords[5].id | https://openalex.org/keywords/physics |
| keywords[5].score | 0.3507355749607086 |
| keywords[5].display_name | Physics |
| keywords[6].id | https://openalex.org/keywords/geometry |
| keywords[6].score | 0.12094458937644958 |
| keywords[6].display_name | Geometry |
| language | en |
| locations[0].id | doi:10.21468/scipostphys.15.4.155 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S4210195687 |
| locations[0].source.issn | 2542-4653 |
| locations[0].source.type | journal |
| locations[0].source.is_oa | True |
| locations[0].source.issn_l | 2542-4653 |
| locations[0].source.is_core | True |
| locations[0].source.is_in_doaj | True |
| locations[0].source.display_name | SciPost Physics |
| locations[0].source.host_organization | https://openalex.org/P4310318585 |
| locations[0].source.host_organization_name | SciPost.org |
| locations[0].source.host_organization_lineage | https://openalex.org/P4310318585 |
| locations[0].source.host_organization_lineage_names | SciPost.org |
| locations[0].license | cc-by |
| locations[0].pdf_url | https://scipost.org/10.21468/SciPostPhys.15.4.155/pdf |
| locations[0].version | publishedVersion |
| locations[0].raw_type | journal-article |
| locations[0].license_id | https://openalex.org/licenses/cc-by |
| locations[0].is_accepted | True |
| locations[0].is_published | True |
| locations[0].raw_source_name | SciPost Physics |
| locations[0].landing_page_url | https://doi.org/10.21468/scipostphys.15.4.155 |
| locations[1].id | pmh:oai:arXiv.org:2304.09886 |
| locations[1].is_oa | True |
| locations[1].source.id | https://openalex.org/S4306400194 |
| locations[1].source.issn | |
| locations[1].source.type | repository |
| locations[1].source.is_oa | True |
| locations[1].source.issn_l | |
| locations[1].source.is_core | False |
| locations[1].source.is_in_doaj | False |
| locations[1].source.display_name | arXiv (Cornell University) |
| locations[1].source.host_organization | https://openalex.org/I205783295 |
| locations[1].source.host_organization_name | Cornell University |
| locations[1].source.host_organization_lineage | https://openalex.org/I205783295 |
| locations[1].license | |
| locations[1].pdf_url | https://arxiv.org/pdf/2304.09886 |
| locations[1].version | submittedVersion |
| locations[1].raw_type | text |
| locations[1].license_id | |
| locations[1].is_accepted | False |
| locations[1].is_published | False |
| locations[1].raw_source_name | |
| locations[1].landing_page_url | http://arxiv.org/abs/2304.09886 |
| locations[2].id | pmh:oai:doaj.org/article:7640808027f8476ca1b24c5bcdf47418 |
| locations[2].is_oa | False |
| locations[2].source.id | https://openalex.org/S4306401280 |
| locations[2].source.issn | |
| locations[2].source.type | repository |
| locations[2].source.is_oa | False |
| locations[2].source.issn_l | |
| locations[2].source.is_core | False |
| locations[2].source.is_in_doaj | False |
| locations[2].source.display_name | DOAJ (DOAJ: Directory of Open Access Journals) |
| locations[2].source.host_organization | |
| locations[2].source.host_organization_name | |
| locations[2].license | |
| locations[2].pdf_url | |
| locations[2].version | submittedVersion |
| locations[2].raw_type | article |
| locations[2].license_id | |
| locations[2].is_accepted | False |
| locations[2].is_published | False |
| locations[2].raw_source_name | SciPost Physics, Vol 15, Iss 4, p 155 (2023) |
| locations[2].landing_page_url | https://doaj.org/article/7640808027f8476ca1b24c5bcdf47418 |
| indexed_in | arxiv, crossref, doaj |
| authorships[0].author.id | https://openalex.org/A5057635387 |
| authorships[0].author.orcid | https://orcid.org/0000-0002-5181-9126 |
| authorships[0].author.display_name | Weiguang Cao |
| authorships[0].countries | JP |
| authorships[0].affiliations[0].institution_ids | https://openalex.org/I74801974 |
| authorships[0].affiliations[0].raw_affiliation_string | Department of Physics, Graduate School of Science, University of Tokyo, Tokyo 113-0033, Japan |
| authorships[0].affiliations[1].institution_ids | https://openalex.org/I166644833, https://openalex.org/I74801974 |
| authorships[0].affiliations[1].raw_affiliation_string | Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa, Chiba 277-8583, Japan |
| authorships[0].institutions[0].id | https://openalex.org/I166644833 |
| authorships[0].institutions[0].ror | https://ror.org/02chw6z69 |
| authorships[0].institutions[0].type | facility |
| authorships[0].institutions[0].lineage | https://openalex.org/I166644833 |
| authorships[0].institutions[0].country_code | JP |
| authorships[0].institutions[0].display_name | Kavli Institute for the Physics and Mathematics of the Universe |
| authorships[0].institutions[1].id | https://openalex.org/I74801974 |
| authorships[0].institutions[1].ror | https://ror.org/057zh3y96 |
| authorships[0].institutions[1].type | education |
| authorships[0].institutions[1].lineage | https://openalex.org/I74801974 |
| authorships[0].institutions[1].country_code | JP |
| authorships[0].institutions[1].display_name | The University of Tokyo |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Weiguang Cao |
| authorships[0].is_corresponding | False |
| authorships[0].raw_affiliation_strings | Department of Physics, Graduate School of Science, University of Tokyo, Tokyo 113-0033, Japan, Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa, Chiba 277-8583, Japan |
| authorships[1].author.id | https://openalex.org/A5093559999 |
| authorships[1].author.orcid | https://orcid.org/0000-0002-8205-6889 |
| authorships[1].author.display_name | Linhao Li |
| authorships[1].countries | JP |
| authorships[1].affiliations[0].institution_ids | https://openalex.org/I74801974 |
| authorships[1].affiliations[0].raw_affiliation_string | Department of Physics, Graduate School of Science, University of Tokyo, Tokyo 113-0033, Japan |
| authorships[1].affiliations[1].institution_ids | https://openalex.org/I74801974 |
| authorships[1].affiliations[1].raw_affiliation_string | Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan |
| authorships[1].institutions[0].id | https://openalex.org/I74801974 |
| authorships[1].institutions[0].ror | https://ror.org/057zh3y96 |
| authorships[1].institutions[0].type | education |
| authorships[1].institutions[0].lineage | https://openalex.org/I74801974 |
| authorships[1].institutions[0].country_code | JP |
| authorships[1].institutions[0].display_name | The University of Tokyo |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | Linhao Li |
| authorships[1].is_corresponding | False |
| authorships[1].raw_affiliation_strings | Department of Physics, Graduate School of Science, University of Tokyo, Tokyo 113-0033, Japan, Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan |
| authorships[2].author.id | https://openalex.org/A5068736151 |
| authorships[2].author.orcid | https://orcid.org/0000-0001-7164-8187 |
| authorships[2].author.display_name | Masahito Yamazaki |
| authorships[2].countries | JP |
| authorships[2].affiliations[0].institution_ids | https://openalex.org/I166644833, https://openalex.org/I74801974 |
| authorships[2].affiliations[0].raw_affiliation_string | Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa, Chiba 277-8583, Japan |
| authorships[2].affiliations[1].institution_ids | https://openalex.org/I74801974 |
| authorships[2].affiliations[1].raw_affiliation_string | Trans-Scale Quantum Science Institute, University of Tokyo, Tokyo 113-0033, Japan |
| authorships[2].institutions[0].id | https://openalex.org/I166644833 |
| authorships[2].institutions[0].ror | https://ror.org/02chw6z69 |
| authorships[2].institutions[0].type | facility |
| authorships[2].institutions[0].lineage | https://openalex.org/I166644833 |
| authorships[2].institutions[0].country_code | JP |
| authorships[2].institutions[0].display_name | Kavli Institute for the Physics and Mathematics of the Universe |
| authorships[2].institutions[1].id | https://openalex.org/I74801974 |
| authorships[2].institutions[1].ror | https://ror.org/057zh3y96 |
| authorships[2].institutions[1].type | education |
| authorships[2].institutions[1].lineage | https://openalex.org/I74801974 |
| authorships[2].institutions[1].country_code | JP |
| authorships[2].institutions[1].display_name | The University of Tokyo |
| authorships[2].author_position | middle |
| authorships[2].raw_author_name | Masahito Yamazaki |
| authorships[2].is_corresponding | False |
| authorships[2].raw_affiliation_strings | Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa, Chiba 277-8583, Japan, Trans-Scale Quantum Science Institute, University of Tokyo, Tokyo 113-0033, Japan |
| authorships[3].author.id | https://openalex.org/A5081365010 |
| authorships[3].author.orcid | https://orcid.org/0000-0002-0365-8225 |
| authorships[3].author.display_name | Yunqin Zheng |
| authorships[3].countries | JP |
| authorships[3].affiliations[0].institution_ids | https://openalex.org/I166644833, https://openalex.org/I74801974 |
| authorships[3].affiliations[0].raw_affiliation_string | Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa, Chiba 277-8583, Japan |
| authorships[3].affiliations[1].institution_ids | https://openalex.org/I74801974 |
| authorships[3].affiliations[1].raw_affiliation_string | Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan |
| authorships[3].institutions[0].id | https://openalex.org/I166644833 |
| authorships[3].institutions[0].ror | https://ror.org/02chw6z69 |
| authorships[3].institutions[0].type | facility |
| authorships[3].institutions[0].lineage | https://openalex.org/I166644833 |
| authorships[3].institutions[0].country_code | JP |
| authorships[3].institutions[0].display_name | Kavli Institute for the Physics and Mathematics of the Universe |
| authorships[3].institutions[1].id | https://openalex.org/I74801974 |
| authorships[3].institutions[1].ror | https://ror.org/057zh3y96 |
| authorships[3].institutions[1].type | education |
| authorships[3].institutions[1].lineage | https://openalex.org/I74801974 |
| authorships[3].institutions[1].country_code | JP |
| authorships[3].institutions[1].display_name | The University of Tokyo |
| authorships[3].author_position | last |
| authorships[3].raw_author_name | Yunqin Zheng |
| authorships[3].is_corresponding | False |
| authorships[3].raw_affiliation_strings | Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan, Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa, Chiba 277-8583, Japan |
| has_content.pdf | True |
| has_content.grobid_xml | True |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://scipost.org/10.21468/SciPostPhys.15.4.155/pdf |
| open_access.oa_status | diamond |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Subsystem non-invertible symmetry operators and defects |
| has_fulltext | True |
| is_retracted | False |
| updated_date | 2025-11-25T14:43:58.451035 |
| primary_topic.id | https://openalex.org/T10792 |
| primary_topic.field.id | https://openalex.org/fields/17 |
| primary_topic.field.display_name | Computer Science |
| primary_topic.score | 0.9983999729156494 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/1703 |
| primary_topic.subfield.display_name | Computational Theory and Mathematics |
| primary_topic.display_name | Matrix Theory and Algorithms |
| related_works | https://openalex.org/W4391375266, https://openalex.org/W4251428025, https://openalex.org/W1979597421, https://openalex.org/W2784467519, https://openalex.org/W4289867043, https://openalex.org/W4231291595, https://openalex.org/W4245609766, https://openalex.org/W1606211735, https://openalex.org/W2329192282, https://openalex.org/W2026588291 |
| cited_by_count | 52 |
| counts_by_year[0].year | 2025 |
| counts_by_year[0].cited_by_count | 23 |
| counts_by_year[1].year | 2024 |
| counts_by_year[1].cited_by_count | 24 |
| counts_by_year[2].year | 2023 |
| counts_by_year[2].cited_by_count | 5 |
| locations_count | 3 |
| best_oa_location.id | doi:10.21468/scipostphys.15.4.155 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S4210195687 |
| best_oa_location.source.issn | 2542-4653 |
| best_oa_location.source.type | journal |
| best_oa_location.source.is_oa | True |
| best_oa_location.source.issn_l | 2542-4653 |
| best_oa_location.source.is_core | True |
| best_oa_location.source.is_in_doaj | True |
| best_oa_location.source.display_name | SciPost Physics |
| best_oa_location.source.host_organization | https://openalex.org/P4310318585 |
| best_oa_location.source.host_organization_name | SciPost.org |
| best_oa_location.source.host_organization_lineage | https://openalex.org/P4310318585 |
| best_oa_location.source.host_organization_lineage_names | SciPost.org |
| best_oa_location.license | cc-by |
| best_oa_location.pdf_url | https://scipost.org/10.21468/SciPostPhys.15.4.155/pdf |
| best_oa_location.version | publishedVersion |
| best_oa_location.raw_type | journal-article |
| best_oa_location.license_id | https://openalex.org/licenses/cc-by |
| best_oa_location.is_accepted | True |
| best_oa_location.is_published | True |
| best_oa_location.raw_source_name | SciPost Physics |
| best_oa_location.landing_page_url | https://doi.org/10.21468/scipostphys.15.4.155 |
| primary_location.id | doi:10.21468/scipostphys.15.4.155 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S4210195687 |
| primary_location.source.issn | 2542-4653 |
| primary_location.source.type | journal |
| primary_location.source.is_oa | True |
| primary_location.source.issn_l | 2542-4653 |
| primary_location.source.is_core | True |
| primary_location.source.is_in_doaj | True |
| primary_location.source.display_name | SciPost Physics |
| primary_location.source.host_organization | https://openalex.org/P4310318585 |
| primary_location.source.host_organization_name | SciPost.org |
| primary_location.source.host_organization_lineage | https://openalex.org/P4310318585 |
| primary_location.source.host_organization_lineage_names | SciPost.org |
| primary_location.license | cc-by |
| primary_location.pdf_url | https://scipost.org/10.21468/SciPostPhys.15.4.155/pdf |
| primary_location.version | publishedVersion |
| primary_location.raw_type | journal-article |
| primary_location.license_id | https://openalex.org/licenses/cc-by |
| primary_location.is_accepted | True |
| primary_location.is_published | True |
| primary_location.raw_source_name | SciPost Physics |
| primary_location.landing_page_url | https://doi.org/10.21468/scipostphys.15.4.155 |
| publication_date | 2023-10-12 |
| publication_year | 2023 |
| referenced_works | https://openalex.org/W2136497493, https://openalex.org/W4281264234, https://openalex.org/W2092760676, https://openalex.org/W2493339491, https://openalex.org/W2556553547, https://openalex.org/W2592119549, https://openalex.org/W2605562043, https://openalex.org/W2726087808, https://openalex.org/W2738241111, https://openalex.org/W2761505211, https://openalex.org/W2770983681, https://openalex.org/W2785656069, https://openalex.org/W2794966645, https://openalex.org/W2951623434, https://openalex.org/W2959199747, https://openalex.org/W2907502928, https://openalex.org/W2969427782, https://openalex.org/W2974457978, https://openalex.org/W2979777761, https://openalex.org/W3008004382, https://openalex.org/W3081741603, https://openalex.org/W2997055532, https://openalex.org/W3083540094, https://openalex.org/W3080588626, https://openalex.org/W3216779031, https://openalex.org/W4210597964, https://openalex.org/W3210489177, https://openalex.org/W3202220941, https://openalex.org/W4378470327, https://openalex.org/W4383293844, https://openalex.org/W4224243714, https://openalex.org/W4307313203, https://openalex.org/W4221143717, https://openalex.org/W4292953076, https://openalex.org/W4308506765, https://openalex.org/W4320449035, https://openalex.org/W4321442622, https://openalex.org/W4309952690, https://openalex.org/W4380184688, https://openalex.org/W4313910219, https://openalex.org/W4316829720, https://openalex.org/W4362703303, https://openalex.org/W4387402082, https://openalex.org/W4383093209, https://openalex.org/W4225539583, https://openalex.org/W2065380813, https://openalex.org/W2002248243, https://openalex.org/W2169919279, https://openalex.org/W2158891124, https://openalex.org/W2003513046, https://openalex.org/W2164624973, https://openalex.org/W2337724348, https://openalex.org/W2606774196, https://openalex.org/W2779033635, https://openalex.org/W2786370293, https://openalex.org/W2993696085, https://openalex.org/W2999589151, https://openalex.org/W3031301686, https://openalex.org/W3175329602, https://openalex.org/W3050554984, https://openalex.org/W3072068184, https://openalex.org/W3204287388, https://openalex.org/W3204553423, https://openalex.org/W3203267487, https://openalex.org/W3210004857, https://openalex.org/W4307023428, https://openalex.org/W4307835724, https://openalex.org/W4366823256, https://openalex.org/W4288055927, https://openalex.org/W4290056231, https://openalex.org/W4324130960, https://openalex.org/W4321231146, https://openalex.org/W4382395520, https://openalex.org/W4362655390, https://openalex.org/W2088356234, https://openalex.org/W2951252175, https://openalex.org/W2937394116, https://openalex.org/W2886207598, https://openalex.org/W2794132465, https://openalex.org/W2980238940, https://openalex.org/W2976090991, https://openalex.org/W2904977742, https://openalex.org/W3102870732, https://openalex.org/W4214940216, https://openalex.org/W3209862152, https://openalex.org/W4225296715, https://openalex.org/W4225531540, https://openalex.org/W4226029336, https://openalex.org/W4293463471, https://openalex.org/W4317497831, https://openalex.org/W4385546012, https://openalex.org/W2027509539, https://openalex.org/W2010617683, https://openalex.org/W2094760062, https://openalex.org/W2904185103, https://openalex.org/W2956297211, https://openalex.org/W4220714297, https://openalex.org/W4381186727, https://openalex.org/W4295107193, https://openalex.org/W4382240913, https://openalex.org/W2947574411, https://openalex.org/W3120837878, https://openalex.org/W3143011231, https://openalex.org/W3172575010, https://openalex.org/W3215606814, https://openalex.org/W3210059093, https://openalex.org/W3210488965, https://openalex.org/W3217405022, https://openalex.org/W4225515463, https://openalex.org/W4378347232, https://openalex.org/W4318151164, https://openalex.org/W4224068915, https://openalex.org/W4377099394, https://openalex.org/W4229051485, https://openalex.org/W4323543793, https://openalex.org/W4280586070, https://openalex.org/W4387138554, https://openalex.org/W4361207520, https://openalex.org/W4302014228, https://openalex.org/W4291964535, https://openalex.org/W4360611418, https://openalex.org/W4308832117, https://openalex.org/W4296960560, https://openalex.org/W4322721156, https://openalex.org/W4306808670, https://openalex.org/W4383557770, https://openalex.org/W4378900951, https://openalex.org/W4309137615, https://openalex.org/W4360612392, https://openalex.org/W4386695422, https://openalex.org/W4387133144, https://openalex.org/W6910559820, https://openalex.org/W4311638736, https://openalex.org/W4313306035, https://openalex.org/W4386074183, https://openalex.org/W4384933192, https://openalex.org/W4313533604, https://openalex.org/W4386744488, https://openalex.org/W4364378690, https://openalex.org/W4323076418, https://openalex.org/W2298547144, https://openalex.org/W3013403132, https://openalex.org/W3017207636, https://openalex.org/W3040942750, https://openalex.org/W3091960035, https://openalex.org/W3097249602, https://openalex.org/W3115170510, https://openalex.org/W3161006064, https://openalex.org/W4384827915, https://openalex.org/W4323669536, https://openalex.org/W4381545948, https://openalex.org/W3200717390, https://openalex.org/W4383604316, https://openalex.org/W4317669083, https://openalex.org/W2939995445, https://openalex.org/W3093096098, https://openalex.org/W2204836735, https://openalex.org/W2901960170, https://openalex.org/W3035925708, https://openalex.org/W3205552539, https://openalex.org/W2781070109, https://openalex.org/W2968123901, https://openalex.org/W4225871814, https://openalex.org/W4382723822, https://openalex.org/W2606930514, https://openalex.org/W3007533810, https://openalex.org/W4308619573, https://openalex.org/W2913335413, https://openalex.org/W3134282431, https://openalex.org/W1844213968, https://openalex.org/W1990577812, https://openalex.org/W1551530254, https://openalex.org/W2120842301, https://openalex.org/W3088585352, https://openalex.org/W3141780685, https://openalex.org/W3204501867, https://openalex.org/W4360951468, https://openalex.org/W4312191530, https://openalex.org/W4361196918, https://openalex.org/W4384111556, https://openalex.org/W2028656212, https://openalex.org/W2021044075, https://openalex.org/W2083202559, https://openalex.org/W2611893150, https://openalex.org/W2945293867, https://openalex.org/W3049733224, https://openalex.org/W4223634974, https://openalex.org/W2971724865, https://openalex.org/W2978081685, https://openalex.org/W4213194173, https://openalex.org/W2097361916, https://openalex.org/W1710401991, https://openalex.org/W2952652949, https://openalex.org/W2914995718, https://openalex.org/W3081727894, https://openalex.org/W3008818137, https://openalex.org/W3155055987, https://openalex.org/W3099855161, https://openalex.org/W3101110574, https://openalex.org/W3100321066, https://openalex.org/W3101696799, https://openalex.org/W3100719054, https://openalex.org/W3106410127, https://openalex.org/W3098422298, https://openalex.org/W3099842170, https://openalex.org/W3104210656, https://openalex.org/W3114467465, https://openalex.org/W3208177527, https://openalex.org/W3099422648, https://openalex.org/W3105759812, https://openalex.org/W3098845406, https://openalex.org/W3122683805, https://openalex.org/W3100204014, https://openalex.org/W3105006732, https://openalex.org/W3104002314, https://openalex.org/W3102618344, https://openalex.org/W3099204515, https://openalex.org/W3100433369, https://openalex.org/W3105493533, https://openalex.org/W3120934623, https://openalex.org/W3099681702, https://openalex.org/W3098639342, https://openalex.org/W3105322095, https://openalex.org/W3194490697, https://openalex.org/W3109299709, https://openalex.org/W3136879073, https://openalex.org/W3156582911, https://openalex.org/W3105217528, https://openalex.org/W3149065489, https://openalex.org/W3101094617, https://openalex.org/W3104902730, https://openalex.org/W3100213535, https://openalex.org/W3104951132, https://openalex.org/W3099813200, https://openalex.org/W3104661943, https://openalex.org/W3124300277, https://openalex.org/W3129803480 |
| referenced_works_count | 237 |
| abstract_inverted_index.a | 23 |
| abstract_inverted_index.By | 67 |
| abstract_inverted_index.We | 0, 21, 105 |
| abstract_inverted_index.by | 56 |
| abstract_inverted_index.in | 4, 94 |
| abstract_inverted_index.of | 63, 74, 101, 111 |
| abstract_inverted_index.on | 58, 108 |
| abstract_inverted_index.or | 61 |
| abstract_inverted_index.we | 70 |
| abstract_inverted_index.The | 48 |
| abstract_inverted_index.Z_2 | 11, 26 |
| abstract_inverted_index.and | 52, 77, 117 |
| abstract_inverted_index.are | 54, 92 |
| abstract_inverted_index.its | 119 |
| abstract_inverted_index.the | 38, 44, 59, 64, 99, 109, 112 |
| abstract_inverted_index.both | 95 |
| abstract_inverted_index.half | 62 |
| abstract_inverted_index.with | 8, 85 |
| abstract_inverted_index.Ising | 82 |
| abstract_inverted_index.rules | 73, 84 |
| abstract_inverted_index.which | 42, 79 |
| abstract_inverted_index.whole | 60 |
| abstract_inverted_index.called | 37 |
| abstract_inverted_index.derive | 71 |
| abstract_inverted_index.fusion | 72, 83 |
| abstract_inverted_index.mobile | 93 |
| abstract_inverted_index.models | 7 |
| abstract_inverted_index.space. | 66 |
| abstract_inverted_index.twice, | 69 |
| abstract_inverted_index.unlike | 98 |
| abstract_inverted_index.Hilbert | 65 |
| abstract_inverted_index.\mathbb | 10, 25 |
| abstract_inverted_index.anomaly | 110 |
| abstract_inverted_index.comment | 107 |
| abstract_inverted_index.defects | 53, 91, 100 |
| abstract_inverted_index.discuss | 118 |
| abstract_inverted_index.duality | 50, 75, 90, 115 |
| abstract_inverted_index.explore | 1 |
| abstract_inverted_index.finally | 106 |
| abstract_inverted_index.gauging | 68 |
| abstract_inverted_index.lattice | 6 |
| abstract_inverted_index.spatial | 96 |
| abstract_inverted_index.-gauging | 35 |
| abstract_inverted_index.defects, | 78 |
| abstract_inverted_index.enriches | 80 |
| abstract_inverted_index.gaugings | 57 |
| abstract_inverted_index.ordinary | 45, 81 |
| abstract_inverted_index.<mml:math | 12, 27 |
| abstract_inverted_index.Subsystem | 88 |
| abstract_inverted_index.features. | 87 |
| abstract_inverted_index.introduce | 22 |
| abstract_inverted_index.operators | 51, 76 |
| abstract_inverted_index.subsystem | 9, 24, 39, 86, 103, 113 |
| abstract_inverted_index.symmetry, | 116 |
| abstract_inverted_index.symmetry. | 20 |
| abstract_inverted_index.<mml:msub> | 15, 30 |
| abstract_inverted_index.invertible | 102 |
| abstract_inverted_index.procedure, | 36 |
| abstract_inverted_index.symmetries | 3 |
| abstract_inverted_index.</mml:math> | 19, 34 |
| abstract_inverted_index.</mml:msub> | 18, 33 |
| abstract_inverted_index.constructed | 55 |
| abstract_inverted_index.directions, | 97 |
| abstract_inverted_index.generalizes | 43 |
| abstract_inverted_index.subtleties. | 120 |
| abstract_inverted_index.symmetries. | 104 |
| abstract_inverted_index.corresponding | 49 |
| abstract_inverted_index.non-invertible | 2 |
| abstract_inverted_index.Kramers-Wannier | 40, 46, 89, 114 |
| abstract_inverted_index.transformation, | 41 |
| abstract_inverted_index.transformation. | 47 |
| abstract_inverted_index.two-dimensional | 5 |
| abstract_inverted_index.display="inline"> | 14, 29 |
| abstract_inverted_index.<mml:mn>2</mml:mn> | 17, 32 |
| abstract_inverted_index.<mml:mi>ℤ</mml:mi> | 16, 31 |
| abstract_inverted_index.xmlns:mml="http://www.w3.org/1998/Math/MathML" | 13, 28 |
| cited_by_percentile_year.max | 100 |
| cited_by_percentile_year.min | 97 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 4 |
| citation_normalized_percentile.value | 0.98980136 |
| citation_normalized_percentile.is_in_top_1_percent | True |
| citation_normalized_percentile.is_in_top_10_percent | True |