Landscapes of integrable long-range spin chains
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910860376539136 |
|---|---|
| author | Klabbers, Rob Lamers, Jules |
| author_facet | Klabbers, Rob Lamers, Jules |
| contents | We clarify how the elliptic integrable spin chain recently found by Matushko and Zotov (MZ) relates to various other known long-range spin chains.
The limit $q\to1$ gives the elliptic spin chain of Sechin and Zotov (SZ), whose trigonometric case is due to Fukui and Kawakami. At finite size, only the latter is U(1)-symmetric.
We compare the resulting (vertex-type) landscape of the MZ chain with the (face-type) landscape containing the Heisenberg XXX and Haldane--Shastry (HS) chains, as well as the Inozemtsev chain and its recent q-deformation. We find that the two landscapes only share a single point: the rational HS chain. Using wrapping we show that the SZ chain is the anti-periodic version of the Inozemtsev chain in a precise sense, and expand both chains around their nearest-neighbour limits to facilitate their interpretations as long-range deformations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09718 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Landscapes of integrable long-range spin chains Klabbers, Rob Lamers, Jules Mathematical Physics Strongly Correlated Electrons High Energy Physics - Theory Exactly Solvable and Integrable Systems We clarify how the elliptic integrable spin chain recently found by Matushko and Zotov (MZ) relates to various other known long-range spin chains. The limit $q\to1$ gives the elliptic spin chain of Sechin and Zotov (SZ), whose trigonometric case is due to Fukui and Kawakami. At finite size, only the latter is U(1)-symmetric. We compare the resulting (vertex-type) landscape of the MZ chain with the (face-type) landscape containing the Heisenberg XXX and Haldane--Shastry (HS) chains, as well as the Inozemtsev chain and its recent q-deformation. We find that the two landscapes only share a single point: the rational HS chain. Using wrapping we show that the SZ chain is the anti-periodic version of the Inozemtsev chain in a precise sense, and expand both chains around their nearest-neighbour limits to facilitate their interpretations as long-range deformations. |
| title | Landscapes of integrable long-range spin chains |
| topic | Mathematical Physics Strongly Correlated Electrons High Energy Physics - Theory Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2405.09718 |