From the XXZ chain to the integrable Rydberg-blockade ladder via non-invertible duality defects
Strongly interacting models often possess "dualities" subtler than a one-to-one mapping of energy levels. The maps can be non-invertible, as apparent in the canonical example of Kramers and Wannier. We analyse an algebraic structure common to the XXZ spin chain and three other models: Rydb...
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| Format: | Journal article |
| Language: | English |
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SciPost
2024
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| _version_ | 1811140700837773312 |
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| author | Eck, L Fendley, P |
| author_facet | Eck, L Fendley, P |
| author_sort | Eck, L |
| collection | OXFORD |
| description | Strongly interacting models often possess "dualities" subtler than a one-to-one mapping of energy levels. The maps can be non-invertible, as apparent in the canonical example of Kramers and Wannier. We analyse an algebraic structure common to the XXZ spin chain and three other models: Rydberg-blockade bosons with one particle per square of a ladder, a three-state antiferromagnet, and two Ising chains coupled in a zigzag fashion. The structure yields non-invertible maps between the four models while also guaranteeing all are integrable. We construct these maps explicitly utilising topological defects coming from fusion categories and the lattice version of the orbifold construction, and use them to give explicit conformal-field-theory partition functions describing their critical regions. The Rydberg and Ising ladders also possess interesting non-invertible symmetries, with the spontaneous breaking of one in the former resulting in an unusual ground-state degeneracy. |
| first_indexed | 2024-09-25T04:26:09Z |
| format | Journal article |
| id | oxford-uuid:33ba3a34-bef1-4a80-80ea-f51331557f57 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:26:09Z |
| publishDate | 2024 |
| publisher | SciPost |
| record_format | dspace |
| spelling | oxford-uuid:33ba3a34-bef1-4a80-80ea-f51331557f572024-08-23T17:22:20ZFrom the XXZ chain to the integrable Rydberg-blockade ladder via non-invertible duality defectsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:33ba3a34-bef1-4a80-80ea-f51331557f57EnglishSymplectic ElementsSciPost2024Eck, LFendley, PStrongly interacting models often possess "dualities" subtler than a one-to-one mapping of energy levels. The maps can be non-invertible, as apparent in the canonical example of Kramers and Wannier. We analyse an algebraic structure common to the XXZ spin chain and three other models: Rydberg-blockade bosons with one particle per square of a ladder, a three-state antiferromagnet, and two Ising chains coupled in a zigzag fashion. The structure yields non-invertible maps between the four models while also guaranteeing all are integrable. We construct these maps explicitly utilising topological defects coming from fusion categories and the lattice version of the orbifold construction, and use them to give explicit conformal-field-theory partition functions describing their critical regions. The Rydberg and Ising ladders also possess interesting non-invertible symmetries, with the spontaneous breaking of one in the former resulting in an unusual ground-state degeneracy. |
| spellingShingle | Eck, L Fendley, P From the XXZ chain to the integrable Rydberg-blockade ladder via non-invertible duality defects |
| title | From the XXZ chain to the integrable Rydberg-blockade ladder via non-invertible duality defects |
| title_full | From the XXZ chain to the integrable Rydberg-blockade ladder via non-invertible duality defects |
| title_fullStr | From the XXZ chain to the integrable Rydberg-blockade ladder via non-invertible duality defects |
| title_full_unstemmed | From the XXZ chain to the integrable Rydberg-blockade ladder via non-invertible duality defects |
| title_short | From the XXZ chain to the integrable Rydberg-blockade ladder via non-invertible duality defects |
| title_sort | from the xxz chain to the integrable rydberg blockade ladder via non invertible duality defects |
| work_keys_str_mv | AT eckl fromthexxzchaintotheintegrablerydbergblockadeladdervianoninvertibledualitydefects AT fendleyp fromthexxzchaintotheintegrablerydbergblockadeladdervianoninvertibledualitydefects |