Engineering Hierarchical Symmetries
The capacity to custom tailor the properties of quantum matter and materials is a central requirement for enlarging their range of possible functionalities. A particularly promising route is the use of driving protocols to engineer specific desired properties with a high degree of control and flexib...
Saved in:
| Published in | Physical review. X Vol. 14; no. 4; p. 041070 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
American Physical Society
01.12.2024
|
| Online Access | Get full text |
| ISSN | 2160-3308 2160-3308 |
| DOI | 10.1103/PhysRevX.14.041070 |
Cover
Loading…
| Abstract | The capacity to custom tailor the properties of quantum matter and materials is a central requirement for enlarging their range of possible functionalities. A particularly promising route is the use of driving protocols to engineer specific desired properties with a high degree of control and flexibility. Here, we present such a program for the tunable generation of sequences of symmetries on controllable timescales. Concretely, our general driving protocol for many-body systems generates a sequence of prethermal regimes, each exhibiting a lower symmetry than the preceding one. We provide an explicit construction of effective Hamiltonians exhibiting these symmetries, which imprints emergent quasiconservation laws hierarchically, enabling us to engineer the respective symmetries and concomitant orders in nonequilibrium matter. We provide explicit examples, including spatiotemporal and topological phenomena, as well as a spin chain realizing the symmetry ladder
SU
(
2
)
→
U
(
1
)
→
Z
2
→
E
. Our results have direct applications in experiments with quantum simulators. |
|---|---|
| AbstractList | The capacity to custom tailor the properties of quantum matter and materials is a central requirement for enlarging their range of possible functionalities. A particularly promising route is the use of driving protocols to engineer specific desired properties with a high degree of control and flexibility. Here, we present such a program for the tunable generation of sequences of symmetries on controllable timescales. Concretely, our general driving protocol for many-body systems generates a sequence of prethermal regimes, each exhibiting a lower symmetry than the preceding one. We provide an explicit construction of effective Hamiltonians exhibiting these symmetries, which imprints emergent quasiconservation laws hierarchically, enabling us to engineer the respective symmetries and concomitant orders in nonequilibrium matter. We provide explicit examples, including spatiotemporal and topological phenomena, as well as a spin chain realizing the symmetry ladder
SU
(
2
)
→
U
(
1
)
→
Z
2
→
E
. Our results have direct applications in experiments with quantum simulators. The capacity to custom tailor the properties of quantum matter and materials is a central requirement for enlarging their range of possible functionalities. A particularly promising route is the use of driving protocols to engineer specific desired properties with a high degree of control and flexibility. Here, we present such a program for the tunable generation of sequences of symmetries on controllable timescales. Concretely, our general driving protocol for many-body systems generates a sequence of prethermal regimes, each exhibiting a lower symmetry than the preceding one. We provide an explicit construction of effective Hamiltonians exhibiting these symmetries, which imprints emergent quasiconservation laws hierarchically, enabling us to engineer the respective symmetries and concomitant orders in nonequilibrium matter. We provide explicit examples, including spatiotemporal and topological phenomena, as well as a spin chain realizing the symmetry ladder SU(2)→U(1)→Z_{2}→E. Our results have direct applications in experiments with quantum simulators. |
| ArticleNumber | 041070 |
| Author | Zhao, Hongzheng Moessner, Roderich Bukov, Marin Fu, Zhanpeng |
| Author_xml | – sequence: 1 givenname: Zhanpeng surname: Fu fullname: Fu, Zhanpeng – sequence: 2 givenname: Roderich surname: Moessner fullname: Moessner, Roderich – sequence: 3 givenname: Hongzheng surname: Zhao fullname: Zhao, Hongzheng – sequence: 4 givenname: Marin orcidid: 0000-0002-3688-9599 surname: Bukov fullname: Bukov, Marin |
| BookMark | eNpN0E1LAzEQgOEgCtbaP-Cp4HnrTJJNukcp1RYKih_gLeRj0qa0u5IUof_ealWcywxzeA7vBTttu5YYu0IYIYK4eVztyxN9vI1QjkAiaDhhPY4KKiFgfPrvPmeDUtZwGAUote6x62m7TC1RTu1yOEuUbfar5O1m-LzfbmmXE5VLdhbtptDgZ_fZ6930ZTKrFg_388ntovIHeldx3TgVnUZB2HgU0onYcD8OQGhrTwSBO1vXrrZBSk8-gPMxas4VUFNr0Wfzoxs6uzbvOW1t3pvOJvP96PLS2LxLfkMmNF4EHgSKupFKOqskt-gbyYnzqOLB4kfL566UTPHPQzBf1cxvNYPSHKuJTwcsYuA |
| Cites_doi | 10.1016/0370-2693(81)90590-6 10.1103/PhysRevLett.131.200201 10.1103/PhysRevResearch.4.043060 10.1103/PhysRevB.97.245122 10.1103/PhysRevLett.125.020504 10.1103/RevModPhys.93.025003 10.1103/PhysRevX.11.041054 10.1103/PhysRevLett.120.050507 10.3390/sym2020609 10.1088/1367-2630/14/7/073007 10.1103/PhysRevB.109.075126 10.1103/PhysRevLett.126.230501 10.1103/PhysRevA.106.022209 10.1103/PhysRevX.9.021013 10.1103/PhysRevLett.116.250401 10.1103/PhysRevX.12.041002 10.1103/PhysRevB.105.144204 10.1103/PhysRevB.85.075125 10.1103/PhysRevX.10.031002 10.1103/PhysRevLett.126.040601 10.1103/PhysRevResearch.6.L042033 10.1038/s41586-021-04257-w 10.1038/s41467-018-03481-9 10.1017/CBO9780511813467 10.1038/nphys3743 10.1103/PhysRevA.89.022118 10.1126/science.aah6442 10.1088/1742-5468/2016/06/064007 10.1038/s41586-022-04854-3 10.1103/PhysRevX.10.041018 10.1038/s41567-021-01277-1 10.1103/PRXQuantum.4.020329 10.1103/PhysRev.86.694 10.1103/PhysRevLett.130.226701 10.1103/PhysRevX.6.021013 10.1103/PhysRevB.104.134308 10.1038/s41567-022-01891-7 10.1103/PhysRevB.100.134302 10.1038/s41467-022-33471-x 10.1103/PRXQuantum.4.020318 10.1103/PhysRevResearch.5.043019 10.1103/PhysRevLett.123.090403 10.1103/PhysRevLett.115.256803 10.1103/PhysRevB.87.155114 10.1103/PhysRevLett.130.140402 10.1038/s41586-022-04853-4 10.1146/annurev-conmatphys-040721-015537 10.1080/00018732.2015.1055918 10.1038/s41534-023-00742-4 10.1103/PhysRevLett.127.140602 10.1038/nature18318 10.1126/science.abd9547 10.1103/PhysRevLett.122.010602 10.1103/PhysRevX.13.031008 10.1103/PhysRevLett.131.130401 10.1080/00018732.2016.1198134 10.1103/PhysRevB.109.064305 10.1103/PhysRevLett.117.090402 10.1103/PhysRevB.95.014112 10.1103/PhysRevB.99.245151 10.1038/s41586-019-1177-4 10.1126/sciadv.aat0346 10.1103/PhysRevB.108.075112 10.1103/PhysRevB.99.104303 10.1103/PhysRevLett.118.030401 10.1103/PhysRevX.10.021032 10.1103/PhysRevLett.131.056502 10.1038/s41567-019-0649-7 10.1103/PhysRevResearch.2.033461 10.1103/PhysRevB.82.235114 10.1103/PRXQuantum.2.010323 10.1103/PRXQuantum.3.020303 10.1103/PhysRevLett.127.050602 10.1103/PhysRevLett.111.021601 10.1016/j.aop.2016.01.012 10.1103/PhysRevX.10.021046 10.1103/PhysRevX.8.031070 10.1146/annurev-conmatphys-031218-013423 10.1103/PhysRevB.103.144307 10.1103/PhysRevB.98.104303 10.1103/PhysRevX.6.041001 10.1103/PhysRevResearch.3.023044 10.1146/annurev-conmatphys-020911-125058 10.1103/PhysRevLett.116.120401 10.1103/PhysRevLett.127.140603 10.1103/PRXQuantum.4.030319 10.1103/PhysRevLett.125.240405 10.1126/science.abk2397 |
| ContentType | Journal Article |
| DBID | AAYXX CITATION DOA |
| DOI | 10.1103/PhysRevX.14.041070 |
| DatabaseName | CrossRef DOAJ Directory of Open Access Journals |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | CrossRef |
| Database_xml | – sequence: 1 dbid: DOA name: DOAJ Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Physics |
| EISSN | 2160-3308 |
| ExternalDocumentID | oai_doaj_org_article_d9c3d2d31359464ba642a1c942e22f6f 10_1103_PhysRevX_14_041070 |
| GroupedDBID | 3MX 5VS 88I AAYXX ABJCF ABSSX ABUWG ADBBV AENEX AFGMR AFKRA AGDNE ALMA_UNASSIGNED_HOLDINGS AUAIK AZQEC BCNDV BENPR BGLVJ CCPQU CITATION DWQXO EBS EJD FRP GNUQQ GROUPED_DOAJ HCIFZ KQ8 M2P M7S M~E OK1 PHGZM PHGZT PIMPY PTHSS ROL S7W PQGLB PUEGO |
| ID | FETCH-LOGICAL-c308t-279b6fb713e19c134b3f92c8d0e1a5cee0d2ba55b5ad44cecd0bcff72260e9573 |
| IEDL.DBID | DOA |
| ISSN | 2160-3308 |
| IngestDate | Wed Aug 27 00:45:26 EDT 2025 Tue Jul 01 01:33:24 EDT 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 4 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c308t-279b6fb713e19c134b3f92c8d0e1a5cee0d2ba55b5ad44cecd0bcff72260e9573 |
| ORCID | 0000-0002-3688-9599 |
| OpenAccessLink | https://doaj.org/article/d9c3d2d31359464ba642a1c942e22f6f |
| ParticipantIDs | doaj_primary_oai_doaj_org_article_d9c3d2d31359464ba642a1c942e22f6f crossref_primary_10_1103_PhysRevX_14_041070 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2024-12-01 |
| PublicationDateYYYYMMDD | 2024-12-01 |
| PublicationDate_xml | – month: 12 year: 2024 text: 2024-12-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationTitle | Physical review. X |
| PublicationYear | 2024 |
| Publisher | American Physical Society |
| Publisher_xml | – name: American Physical Society |
| References | PhysRevX.14.041070Cc10R1 PhysRevX.14.041070Cc33R1 PhysRevX.14.041070Cc56R1 PhysRevX.14.041070Cc79R1 PhysRevX.14.041070Cc31R1 PhysRevX.14.041070Cc80R1 PhysRevX.14.041070Cc4R1 PhysRevX.14.041070Cc84R1 PhysRevX.14.041070Cc28R1 PhysRevX.14.041070Cc40R1 PhysRevX.14.041070Cc61R1 PhysRevX.14.041070Cc82R1 L. D. Landau (PhysRevX.14.041070Cc1R1) 2013 PhysRevX.14.041070Cc26R1 PhysRevX.14.041070Cc8R1 PhysRevX.14.041070Cc42R1 PhysRevX.14.041070Cc63R1 PhysRevX.14.041070Cc88R1 PhysRevX.14.041070Cc24R1 PhysRevX.14.041070Cc6R1 PhysRevX.14.041070Cc44R1 PhysRevX.14.041070Cc86R1 PhysRevX.14.041070Cc45R1 PhysRevX.14.041070Cc21R1 PhysRevX.14.041070Cc47R1 PhysRevX.14.041070Cc89R1 PhysRevX.14.041070Cc49R1 PhysRevX.14.041070Cc90R1 PhysRevX.14.041070Cc18R1 PhysRevX.14.041070Cc71R1 PhysRevX.14.041070Cc94R1 PhysRevX.14.041070Cc16R1 PhysRevX.14.041070Cc39R1 PhysRevX.14.041070Cc50R1 PhysRevX.14.041070Cc73R1 PhysRevX.14.041070Cc92R1 PhysRevX.14.041070Cc14R1 PhysRevX.14.041070Cc37R1 PhysRevX.14.041070Cc52R1 PhysRevX.14.041070Cc98R1 PhysRevX.14.041070Cc12R1 PhysRevX.14.041070Cc35R1 PhysRevX.14.041070Cc54R1 PhysRevX.14.041070Cc96R1 PhysRevX.14.041070Cc11R1 PhysRevX.14.041070Cc32R1 PhysRevX.14.041070Cc57R1 PhysRevX.14.041070Cc78R1 PhysRevX.14.041070Cc30R1 PhysRevX.14.041070Cc59R1 PhysRevX.14.041070Cc9R1 PhysRevX.14.041070Cc3R1 PhysRevX.14.041070Cc60R1 PhysRevX.14.041070Cc83R1 PhysRevX.14.041070Cc29R1 PhysRevX.14.041070Cc81R1 PhysRevX.14.041070Cc27R1 PhysRevX.14.041070Cc7R1 PhysRevX.14.041070Cc41R1 PhysRevX.14.041070Cc64R1 PhysRevX.14.041070Cc25R1 PhysRevX.14.041070Cc5R1 PhysRevX.14.041070Cc43R1 PhysRevX.14.041070Cc85R1 PhysRevX.14.041070Cc23R1 PhysRevX.14.041070Cc22R1 PhysRevX.14.041070Cc46R1 PhysRevX.14.041070Cc20R1 PhysRevX.14.041070Cc48R1 PhysRevX.14.041070Cc69R1 PhysRevX.14.041070Cc91R1 PhysRevX.14.041070Cc19R1 PhysRevX.14.041070Cc70R1 PhysRevX.14.041070Cc95R1 PhysRevX.14.041070Cc17R1 PhysRevX.14.041070Cc38R1 PhysRevX.14.041070Cc51R1 PhysRevX.14.041070Cc72R1 PhysRevX.14.041070Cc93R1 PhysRevX.14.041070Cc15R1 PhysRevX.14.041070Cc36R1 PhysRevX.14.041070Cc53R1 PhysRevX.14.041070Cc74R1 P. M. Chaikin (PhysRevX.14.041070Cc2R1) 1995 PhysRevX.14.041070Cc13R1 PhysRevX.14.041070Cc34R1 PhysRevX.14.041070Cc55R1 PhysRevX.14.041070Cc76R1 PhysRevX.14.041070Cc97R1 |
| References_xml | – ident: PhysRevX.14.041070Cc6R1 doi: 10.1016/0370-2693(81)90590-6 – ident: PhysRevX.14.041070Cc80R1 doi: 10.1103/PhysRevLett.131.200201 – ident: PhysRevX.14.041070Cc54R1 doi: 10.1103/PhysRevResearch.4.043060 – ident: PhysRevX.14.041070Cc35R1 doi: 10.1103/PhysRevB.97.245122 – ident: PhysRevX.14.041070Cc13R1 doi: 10.1103/PhysRevLett.125.020504 – ident: PhysRevX.14.041070Cc11R1 doi: 10.1103/RevModPhys.93.025003 – ident: PhysRevX.14.041070Cc14R1 doi: 10.1103/PhysRevX.11.041054 – ident: PhysRevX.14.041070Cc63R1 doi: 10.1103/PhysRevLett.120.050507 – ident: PhysRevX.14.041070Cc7R1 doi: 10.3390/sym2020609 – ident: PhysRevX.14.041070Cc93R1 doi: 10.1088/1367-2630/14/7/073007 – ident: PhysRevX.14.041070Cc18R1 doi: 10.1103/PhysRevB.109.075126 – ident: PhysRevX.14.041070Cc46R1 doi: 10.1103/PhysRevLett.126.230501 – ident: PhysRevX.14.041070Cc57R1 doi: 10.1103/PhysRevA.106.022209 – ident: PhysRevX.14.041070Cc70R1 doi: 10.1103/PhysRevX.9.021013 – ident: PhysRevX.14.041070Cc25R1 doi: 10.1103/PhysRevLett.116.250401 – ident: PhysRevX.14.041070Cc36R1 doi: 10.1103/PhysRevX.12.041002 – ident: PhysRevX.14.041070Cc53R1 doi: 10.1103/PhysRevB.105.144204 – ident: PhysRevX.14.041070Cc3R1 doi: 10.1103/PhysRevB.85.075125 – ident: PhysRevX.14.041070Cc44R1 doi: 10.1103/PhysRevX.10.031002 – ident: PhysRevX.14.041070Cc56R1 doi: 10.1103/PhysRevLett.126.040601 – ident: PhysRevX.14.041070Cc76R1 doi: 10.1103/PhysRevResearch.6.L042033 – ident: PhysRevX.14.041070Cc31R1 doi: 10.1038/s41586-021-04257-w – ident: PhysRevX.14.041070Cc34R1 doi: 10.1038/s41467-018-03481-9 – volume-title: Principles of Condensed Matter Physics year: 1995 ident: PhysRevX.14.041070Cc2R1 doi: 10.1017/CBO9780511813467 – ident: PhysRevX.14.041070Cc41R1 doi: 10.1038/nphys3743 – ident: PhysRevX.14.041070Cc84R1 doi: 10.1103/PhysRevA.89.022118 – ident: PhysRevX.14.041070Cc98R1 doi: 10.1126/science.aah6442 – ident: PhysRevX.14.041070Cc33R1 doi: 10.1088/1742-5468/2016/06/064007 – ident: PhysRevX.14.041070Cc30R1 doi: 10.1038/s41586-022-04854-3 – ident: PhysRevX.14.041070Cc78R1 doi: 10.1103/PhysRevX.10.041018 – ident: PhysRevX.14.041070Cc81R1 doi: 10.1038/s41567-021-01277-1 – ident: PhysRevX.14.041070Cc21R1 doi: 10.1103/PRXQuantum.4.020329 – ident: PhysRevX.14.041070Cc5R1 doi: 10.1103/PhysRev.86.694 – ident: PhysRevX.14.041070Cc20R1 doi: 10.1103/PhysRevLett.130.226701 – ident: PhysRevX.14.041070Cc24R1 doi: 10.1103/PhysRevX.6.021013 – ident: PhysRevX.14.041070Cc95R1 doi: 10.1103/PhysRevB.104.134308 – ident: PhysRevX.14.041070Cc40R1 doi: 10.1038/s41567-022-01891-7 – ident: PhysRevX.14.041070Cc49R1 doi: 10.1103/PhysRevB.100.134302 – ident: PhysRevX.14.041070Cc74R1 doi: 10.1038/s41467-022-33471-x – ident: PhysRevX.14.041070Cc38R1 doi: 10.1103/PRXQuantum.4.020318 – ident: PhysRevX.14.041070Cc94R1 doi: 10.1103/PhysRevResearch.5.043019 – ident: PhysRevX.14.041070Cc42R1 doi: 10.1103/PhysRevLett.123.090403 – ident: PhysRevX.14.041070Cc9R1 doi: 10.1103/PhysRevLett.115.256803 – ident: PhysRevX.14.041070Cc4R1 doi: 10.1103/PhysRevB.87.155114 – ident: PhysRevX.14.041070Cc37R1 doi: 10.1103/PhysRevLett.130.140402 – ident: PhysRevX.14.041070Cc29R1 doi: 10.1038/s41586-022-04853-4 – ident: PhysRevX.14.041070Cc86R1 doi: 10.1146/annurev-conmatphys-040721-015537 – ident: PhysRevX.14.041070Cc59R1 doi: 10.1080/00018732.2015.1055918 – ident: PhysRevX.14.041070Cc47R1 doi: 10.1038/s41534-023-00742-4 – ident: PhysRevX.14.041070Cc89R1 doi: 10.1103/PhysRevLett.127.140602 – ident: PhysRevX.14.041070Cc12R1 doi: 10.1038/nature18318 – ident: PhysRevX.14.041070Cc17R1 doi: 10.1126/science.abd9547 – ident: PhysRevX.14.041070Cc88R1 doi: 10.1103/PhysRevLett.122.010602 – ident: PhysRevX.14.041070Cc19R1 doi: 10.1103/PhysRevX.13.031008 – ident: PhysRevX.14.041070Cc55R1 doi: 10.1103/PhysRevLett.131.130401 – ident: PhysRevX.14.041070Cc32R1 doi: 10.1080/00018732.2016.1198134 – ident: PhysRevX.14.041070Cc92R1 doi: 10.1103/PhysRevB.109.064305 – ident: PhysRevX.14.041070Cc26R1 doi: 10.1103/PhysRevLett.117.090402 – ident: PhysRevX.14.041070Cc61R1 doi: 10.1103/PhysRevB.95.014112 – ident: PhysRevX.14.041070Cc71R1 doi: 10.1103/PhysRevB.99.245151 – ident: PhysRevX.14.041070Cc43R1 doi: 10.1038/s41586-019-1177-4 – ident: PhysRevX.14.041070Cc73R1 doi: 10.1126/sciadv.aat0346 – ident: PhysRevX.14.041070Cc96R1 doi: 10.1103/PhysRevB.108.075112 – ident: PhysRevX.14.041070Cc69R1 doi: 10.1103/PhysRevB.99.104303 – ident: PhysRevX.14.041070Cc27R1 doi: 10.1103/PhysRevLett.118.030401 – ident: PhysRevX.14.041070Cc28R1 doi: 10.1103/PhysRevX.10.021032 – ident: PhysRevX.14.041070Cc91R1 doi: 10.1103/PhysRevLett.131.056502 – volume-title: Statistical Physics year: 2013 ident: PhysRevX.14.041070Cc1R1 – ident: PhysRevX.14.041070Cc16R1 doi: 10.1038/s41567-019-0649-7 – ident: PhysRevX.14.041070Cc50R1 doi: 10.1103/PhysRevResearch.2.033461 – ident: PhysRevX.14.041070Cc22R1 doi: 10.1103/PhysRevB.82.235114 – ident: PhysRevX.14.041070Cc45R1 doi: 10.1103/PRXQuantum.2.010323 – ident: PhysRevX.14.041070Cc64R1 doi: 10.1103/PRXQuantum.3.020303 – ident: PhysRevX.14.041070Cc52R1 doi: 10.1103/PhysRevLett.127.050602 – ident: PhysRevX.14.041070Cc83R1 doi: 10.1103/PhysRevLett.111.021601 – ident: PhysRevX.14.041070Cc10R1 doi: 10.1016/j.aop.2016.01.012 – ident: PhysRevX.14.041070Cc39R1 doi: 10.1103/PhysRevX.10.021046 – ident: PhysRevX.14.041070Cc72R1 doi: 10.1103/PhysRevX.8.031070 – ident: PhysRevX.14.041070Cc15R1 doi: 10.1146/annurev-conmatphys-031218-013423 – ident: PhysRevX.14.041070Cc97R1 doi: 10.1103/PhysRevB.103.144307 – ident: PhysRevX.14.041070Cc85R1 doi: 10.1103/PhysRevB.98.104303 – ident: PhysRevX.14.041070Cc23R1 doi: 10.1103/PhysRevX.6.041001 – ident: PhysRevX.14.041070Cc51R1 doi: 10.1103/PhysRevResearch.3.023044 – ident: PhysRevX.14.041070Cc8R1 doi: 10.1146/annurev-conmatphys-020911-125058 – ident: PhysRevX.14.041070Cc60R1 doi: 10.1103/PhysRevLett.116.120401 – ident: PhysRevX.14.041070Cc90R1 doi: 10.1103/PhysRevLett.127.140603 – ident: PhysRevX.14.041070Cc48R1 doi: 10.1103/PRXQuantum.4.030319 – ident: PhysRevX.14.041070Cc79R1 doi: 10.1103/PhysRevLett.125.240405 – ident: PhysRevX.14.041070Cc82R1 doi: 10.1126/science.abk2397 |
| SSID | ssj0000601477 |
| Score | 2.3876505 |
| Snippet | The capacity to custom tailor the properties of quantum matter and materials is a central requirement for enlarging their range of possible functionalities. A... |
| SourceID | doaj crossref |
| SourceType | Open Website Index Database |
| StartPage | 041070 |
| Title | Engineering Hierarchical Symmetries |
| URI | https://doaj.org/article/d9c3d2d31359464ba642a1c942e22f6f |
| Volume | 14 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LSwMxEA4iCF7EJ9YXC3qT2Gwem81RxVIEPaiF3pY8JiDYKrYK_nsn2VbWkxevYQnZGfi-b2DmG0LObM2U00pT7SWjkjtBrbGGIveAUAEqztKg8N19NRzJ27Ead1Z9pZ6w1h64DVw_GC8CD6IUyshKOouC2ZbeSA6cxyom9EXO6xRTLQaj9Nd6OSXDRD81VD7A5xih4YJJLHrYLybqGPZnZhlsko2FJCwu26dskRWYbpO13JrpZzvktGMZWAyf08Bw3l_yUjx-TSZ5IdZsl4wGN0_XQ7pYbUC9YPWccm1cFR1WiFAaXwrpRDTc14FBaRUSFwvcWaWcskFKDz4w52PUKJYYGKXFHlmdvk5hnxR1kFaH6CrNQXofLKKvKSNwA8jHWvTI-fI3m7fWwaLJyp-JZhkULACaNig9cpUi8fNlcp_OB5iTZpGT5q-cHPzHJYdknaOAaFtHjsjq_P0DjlEAzN1JzvU3gcGtrA |
| linkProvider | Directory of Open Access Journals |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Engineering+Hierarchical+Symmetries&rft.jtitle=Physical+review.+X&rft.au=Fu%2C+Zhanpeng&rft.au=Moessner%2C+Roderich&rft.au=Zhao%2C+Hongzheng&rft.au=Bukov%2C+Marin&rft.date=2024-12-01&rft.issn=2160-3308&rft.eissn=2160-3308&rft.volume=14&rft.issue=4&rft_id=info:doi/10.1103%2FPhysRevX.14.041070&rft.externalDBID=n%2Fa&rft.externalDocID=10_1103_PhysRevX_14_041070 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2160-3308&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2160-3308&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2160-3308&client=summon |