Twisted locality-preserving automorphisms, anomaly index, and generalized Lieb-Schultz-Mattis theorems with anti-unitary symmetries Article Swipe
R. Liu
,
Jinmin Yi
,
Liujun Zou
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2510.06555
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2510.06555
Symmetries and their anomalies are powerful tools to understand quantum matter. In this work, for quantum spin chains, we define twisted locality-preserving automorphisms and their Gross-Nesme-Vogts-Werner indices, which provide a unified framework to describe both unitary and anti-unitary symmetries, on-site and non-on-site symmetries, and internal and translation symmetries. For a symmetry $G$ with actions given by twisted locality-preserving automorphisms, we give a microscopic definition of its anomaly index, which is an element in $H^3_φ(G; U(1))$, where the subscript $φ$ means that anti-unitary elements of $G$ act on $U(1)$ by complex conjugation. We show that an anomalous symmetry leads to multiple Lieb-Schultz-Matttis-type theorems. In particular, any state with an anomalous symmetry must either have long-range correlation or violate the entanglement area law. Based on this theorem, we further deduce that any state with an anomalous symmetry must have long-range entanglement, and any Hamiltonian that has an anomalous symmetry cannot have a unique gapped symmetric ground state, as long as the interactions in the Hamiltonian decay fast enough as the range of the interaction increases. For Hamiltonians with only two-spin interactions, the last theorem holds if the interactions decay faster than $1/r^2$, where $r$ is the distance between the two interacting spins. We demonstrate these general theorems in various concrete examples.
Related Topics
Concepts
No concepts available.
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2510.06555
- https://arxiv.org/pdf/2510.06555
- OA Status
- green
- OpenAlex ID
- https://openalex.org/W4415315894
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4415315894Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.48550/arxiv.2510.06555Digital Object Identifier
- Title
-
Twisted locality-preserving automorphisms, anomaly index, and generalized Lieb-Schultz-Mattis theorems with anti-unitary symmetriesWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2025Year of publication
- Publication date
-
2025-10-08Full publication date if available
- Authors
-
R. Liu, Jinmin Yi, Liujun ZouList of authors in order
- Landing page
-
https://arxiv.org/abs/2510.06555Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2510.06555Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2510.06555Direct OA link when available
- Cited by
-
0Total citation count in OpenAlex
Full payload
| id | https://openalex.org/W4415315894 |
|---|---|
| doi | https://doi.org/10.48550/arxiv.2510.06555 |
| ids.doi | https://doi.org/10.48550/arxiv.2510.06555 |
| ids.openalex | https://openalex.org/W4415315894 |
| fwci | |
| type | preprint |
| title | Twisted locality-preserving automorphisms, anomaly index, and generalized Lieb-Schultz-Mattis theorems with anti-unitary symmetries |
| biblio.issue | |
| biblio.volume | |
| biblio.last_page | |
| biblio.first_page | |
| topics[0].id | https://openalex.org/T11476 |
| topics[0].field.id | https://openalex.org/fields/26 |
| topics[0].field.display_name | Mathematics |
| topics[0].score | 0.98089998960495 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/2608 |
| topics[0].subfield.display_name | Geometry and Topology |
| topics[0].display_name | Graph theory and applications |
| topics[1].id | https://openalex.org/T11261 |
| topics[1].field.id | https://openalex.org/fields/31 |
| topics[1].field.display_name | Physics and Astronomy |
| topics[1].score | 0.9728000164031982 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/3109 |
| topics[1].subfield.display_name | Statistical and Nonlinear Physics |
| topics[1].display_name | Quantum chaos and dynamical systems |
| topics[2].id | https://openalex.org/T11022 |
| topics[2].field.id | https://openalex.org/fields/26 |
| topics[2].field.display_name | Mathematics |
| topics[2].score | 0.9704999923706055 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/2610 |
| topics[2].subfield.display_name | Mathematical Physics |
| topics[2].display_name | Spectral Theory in Mathematical Physics |
| is_xpac | False |
| apc_list | |
| apc_paid | |
| language | en |
| locations[0].id | pmh:oai:arXiv.org:2510.06555 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S4306400194 |
| locations[0].source.issn | |
| locations[0].source.type | repository |
| locations[0].source.is_oa | True |
| locations[0].source.issn_l | |
| locations[0].source.is_core | False |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | arXiv (Cornell University) |
| locations[0].source.host_organization | https://openalex.org/I205783295 |
| locations[0].source.host_organization_name | Cornell University |
| locations[0].source.host_organization_lineage | https://openalex.org/I205783295 |
| locations[0].license | cc-by |
| locations[0].pdf_url | https://arxiv.org/pdf/2510.06555 |
| locations[0].version | submittedVersion |
| locations[0].raw_type | text |
| locations[0].license_id | https://openalex.org/licenses/cc-by |
| locations[0].is_accepted | False |
| locations[0].is_published | False |
| locations[0].raw_source_name | |
| locations[0].landing_page_url | http://arxiv.org/abs/2510.06555 |
| locations[1].id | doi:10.48550/arxiv.2510.06555 |
| 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 | cc-by |
| locations[1].pdf_url | |
| locations[1].version | |
| locations[1].raw_type | article |
| locations[1].license_id | https://openalex.org/licenses/cc-by |
| locations[1].is_accepted | False |
| locations[1].is_published | |
| locations[1].raw_source_name | |
| locations[1].landing_page_url | https://doi.org/10.48550/arxiv.2510.06555 |
| indexed_in | arxiv, datacite |
| authorships[0].author.id | https://openalex.org/A5111063148 |
| authorships[0].author.orcid | https://orcid.org/0009-0009-3879-7565 |
| authorships[0].author.display_name | R. Liu |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Liu, Ruizhi |
| authorships[0].is_corresponding | False |
| authorships[1].author.id | https://openalex.org/A5025005090 |
| authorships[1].author.orcid | https://orcid.org/0000-0001-6948-2464 |
| authorships[1].author.display_name | Jinmin Yi |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | Yi, Jinmin |
| authorships[1].is_corresponding | False |
| authorships[2].author.id | https://openalex.org/A5086376935 |
| authorships[2].author.orcid | https://orcid.org/0000-0002-6666-4163 |
| authorships[2].author.display_name | Liujun Zou |
| authorships[2].author_position | last |
| authorships[2].raw_author_name | Zou, Liujun |
| authorships[2].is_corresponding | False |
| has_content.pdf | True |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://arxiv.org/pdf/2510.06555 |
| open_access.oa_status | green |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-18T00:00:00 |
| display_name | Twisted locality-preserving automorphisms, anomaly index, and generalized Lieb-Schultz-Mattis theorems with anti-unitary symmetries |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-06T06:51:31.235846 |
| primary_topic.id | https://openalex.org/T11476 |
| primary_topic.field.id | https://openalex.org/fields/26 |
| primary_topic.field.display_name | Mathematics |
| primary_topic.score | 0.98089998960495 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/2608 |
| primary_topic.subfield.display_name | Geometry and Topology |
| primary_topic.display_name | Graph theory and applications |
| cited_by_count | 0 |
| locations_count | 2 |
| best_oa_location.id | pmh:oai:arXiv.org:2510.06555 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S4306400194 |
| best_oa_location.source.issn | |
| best_oa_location.source.type | repository |
| best_oa_location.source.is_oa | True |
| best_oa_location.source.issn_l | |
| best_oa_location.source.is_core | False |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | arXiv (Cornell University) |
| best_oa_location.source.host_organization | https://openalex.org/I205783295 |
| best_oa_location.source.host_organization_name | Cornell University |
| best_oa_location.source.host_organization_lineage | https://openalex.org/I205783295 |
| best_oa_location.license | cc-by |
| best_oa_location.pdf_url | https://arxiv.org/pdf/2510.06555 |
| best_oa_location.version | submittedVersion |
| best_oa_location.raw_type | text |
| best_oa_location.license_id | https://openalex.org/licenses/cc-by |
| best_oa_location.is_accepted | False |
| best_oa_location.is_published | False |
| best_oa_location.raw_source_name | |
| best_oa_location.landing_page_url | http://arxiv.org/abs/2510.06555 |
| primary_location.id | pmh:oai:arXiv.org:2510.06555 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S4306400194 |
| primary_location.source.issn | |
| primary_location.source.type | repository |
| primary_location.source.is_oa | True |
| primary_location.source.issn_l | |
| primary_location.source.is_core | False |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | arXiv (Cornell University) |
| primary_location.source.host_organization | https://openalex.org/I205783295 |
| primary_location.source.host_organization_name | Cornell University |
| primary_location.source.host_organization_lineage | https://openalex.org/I205783295 |
| primary_location.license | cc-by |
| primary_location.pdf_url | https://arxiv.org/pdf/2510.06555 |
| primary_location.version | submittedVersion |
| primary_location.raw_type | text |
| primary_location.license_id | https://openalex.org/licenses/cc-by |
| primary_location.is_accepted | False |
| primary_location.is_published | False |
| primary_location.raw_source_name | |
| primary_location.landing_page_url | http://arxiv.org/abs/2510.06555 |
| publication_date | 2025-10-08 |
| publication_year | 2025 |
| referenced_works_count | 0 |
| abstract_inverted_index.a | 29, 49, 61, 149 |
| abstract_inverted_index.In | 11, 102 |
| abstract_inverted_index.We | 91, 200 |
| abstract_inverted_index.an | 70, 94, 107, 132, 144 |
| abstract_inverted_index.as | 155, 157, 166 |
| abstract_inverted_index.by | 55, 88 |
| abstract_inverted_index.if | 183 |
| abstract_inverted_index.in | 72, 160, 205 |
| abstract_inverted_index.is | 69, 192 |
| abstract_inverted_index.of | 64, 83, 169 |
| abstract_inverted_index.on | 86, 122 |
| abstract_inverted_index.or | 115 |
| abstract_inverted_index.to | 7, 32, 98 |
| abstract_inverted_index.we | 18, 59, 125 |
| abstract_inverted_index.$G$ | 51, 84 |
| abstract_inverted_index.$r$ | 191 |
| abstract_inverted_index.For | 48, 173 |
| abstract_inverted_index.act | 85 |
| abstract_inverted_index.and | 1, 23, 36, 40, 43, 45, 139 |
| abstract_inverted_index.any | 104, 129, 140 |
| abstract_inverted_index.are | 4 |
| abstract_inverted_index.for | 14 |
| abstract_inverted_index.has | 143 |
| abstract_inverted_index.its | 65 |
| abstract_inverted_index.the | 76, 117, 158, 161, 167, 170, 179, 184, 193, 196 |
| abstract_inverted_index.two | 197 |
| abstract_inverted_index.$φ$ | 78 |
| abstract_inverted_index.area | 119 |
| abstract_inverted_index.both | 34 |
| abstract_inverted_index.fast | 164 |
| abstract_inverted_index.give | 60 |
| abstract_inverted_index.have | 112, 136, 148 |
| abstract_inverted_index.last | 180 |
| abstract_inverted_index.law. | 120 |
| abstract_inverted_index.long | 156 |
| abstract_inverted_index.must | 110, 135 |
| abstract_inverted_index.only | 176 |
| abstract_inverted_index.show | 92 |
| abstract_inverted_index.spin | 16 |
| abstract_inverted_index.than | 188 |
| abstract_inverted_index.that | 80, 93, 128, 142 |
| abstract_inverted_index.this | 12, 123 |
| abstract_inverted_index.with | 52, 106, 131, 175 |
| abstract_inverted_index.Based | 121 |
| abstract_inverted_index.decay | 163, 186 |
| abstract_inverted_index.given | 54 |
| abstract_inverted_index.holds | 182 |
| abstract_inverted_index.leads | 97 |
| abstract_inverted_index.means | 79 |
| abstract_inverted_index.range | 168 |
| abstract_inverted_index.state | 105, 130 |
| abstract_inverted_index.their | 2, 24 |
| abstract_inverted_index.these | 202 |
| abstract_inverted_index.tools | 6 |
| abstract_inverted_index.where | 75, 190 |
| abstract_inverted_index.which | 27, 68 |
| abstract_inverted_index.work, | 13 |
| abstract_inverted_index.$U(1)$ | 87 |
| abstract_inverted_index.cannot | 147 |
| abstract_inverted_index.deduce | 127 |
| abstract_inverted_index.define | 19 |
| abstract_inverted_index.either | 111 |
| abstract_inverted_index.enough | 165 |
| abstract_inverted_index.faster | 187 |
| abstract_inverted_index.gapped | 151 |
| abstract_inverted_index.ground | 153 |
| abstract_inverted_index.index, | 67 |
| abstract_inverted_index.spins. | 199 |
| abstract_inverted_index.state, | 154 |
| abstract_inverted_index.unique | 150 |
| abstract_inverted_index.U(1))$, | 74 |
| abstract_inverted_index.actions | 53 |
| abstract_inverted_index.anomaly | 66 |
| abstract_inverted_index.between | 195 |
| abstract_inverted_index.chains, | 17 |
| abstract_inverted_index.complex | 89 |
| abstract_inverted_index.element | 71 |
| abstract_inverted_index.further | 126 |
| abstract_inverted_index.general | 203 |
| abstract_inverted_index.matter. | 10 |
| abstract_inverted_index.on-site | 39 |
| abstract_inverted_index.provide | 28 |
| abstract_inverted_index.quantum | 9, 15 |
| abstract_inverted_index.theorem | 181 |
| abstract_inverted_index.twisted | 20, 56 |
| abstract_inverted_index.unified | 30 |
| abstract_inverted_index.unitary | 35 |
| abstract_inverted_index.various | 206 |
| abstract_inverted_index.violate | 116 |
| abstract_inverted_index.$1/r^2$, | 189 |
| abstract_inverted_index.concrete | 207 |
| abstract_inverted_index.describe | 33 |
| abstract_inverted_index.distance | 194 |
| abstract_inverted_index.elements | 82 |
| abstract_inverted_index.indices, | 26 |
| abstract_inverted_index.internal | 44 |
| abstract_inverted_index.multiple | 99 |
| abstract_inverted_index.powerful | 5 |
| abstract_inverted_index.symmetry | 50, 96, 109, 134, 146 |
| abstract_inverted_index.theorem, | 124 |
| abstract_inverted_index.theorems | 204 |
| abstract_inverted_index.two-spin | 177 |
| abstract_inverted_index.anomalies | 3 |
| abstract_inverted_index.anomalous | 95, 108, 133, 145 |
| abstract_inverted_index.examples. | 208 |
| abstract_inverted_index.framework | 31 |
| abstract_inverted_index.subscript | 77 |
| abstract_inverted_index.symmetric | 152 |
| abstract_inverted_index.theorems. | 101 |
| abstract_inverted_index.$H^3_φ(G; | 73 |
| abstract_inverted_index.Symmetries | 0 |
| abstract_inverted_index.definition | 63 |
| abstract_inverted_index.increases. | 172 |
| abstract_inverted_index.long-range | 113, 137 |
| abstract_inverted_index.understand | 8 |
| abstract_inverted_index.Hamiltonian | 141, 162 |
| abstract_inverted_index.correlation | 114 |
| abstract_inverted_index.demonstrate | 201 |
| abstract_inverted_index.interacting | 198 |
| abstract_inverted_index.interaction | 171 |
| abstract_inverted_index.microscopic | 62 |
| abstract_inverted_index.non-on-site | 41 |
| abstract_inverted_index.particular, | 103 |
| abstract_inverted_index.symmetries, | 38, 42 |
| abstract_inverted_index.symmetries. | 47 |
| abstract_inverted_index.translation | 46 |
| abstract_inverted_index.Hamiltonians | 174 |
| abstract_inverted_index.anti-unitary | 37, 81 |
| abstract_inverted_index.conjugation. | 90 |
| abstract_inverted_index.entanglement | 118 |
| abstract_inverted_index.interactions | 159, 185 |
| abstract_inverted_index.automorphisms | 22 |
| abstract_inverted_index.entanglement, | 138 |
| abstract_inverted_index.interactions, | 178 |
| abstract_inverted_index.automorphisms, | 58 |
| abstract_inverted_index.locality-preserving | 21, 57 |
| abstract_inverted_index.Gross-Nesme-Vogts-Werner | 25 |
| abstract_inverted_index.Lieb-Schultz-Matttis-type | 100 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile |