Preprint

PUBDB-2024-01515

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Landscapes of integrable long-range spin chains

Klabbers, R. ; Lamers, J. (Corresponding author)DESY*

2024

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Please use a persistent id in citations: doi:10.3204/PUBDB-2024-01515

Report No.: DESY-24-062; arXiv:2405.09718

Abstract: We clarify how the elliptic integrable spin chain recently found by Matushko and Zotov (MZ) relates to various other known long-range spin chains. We evaluate various limits. More precisely, we tweak the MZ chain to allow for a short-range limit, and show it is the XX model with q-deformed antiperiodic boundary conditions. Taking $q\to 1$ gives the elliptic spin chain of Sechin and Zotov (SZ), whose trigonometric case is due to Fukui and Kawakami. It, too, can be adjusted to admit a short-range limit, which we demonstrate to be the antiperiodic XX model. By identifying the translation operator of the MZ chain, which is nontrivial, we show that antiperiodicity is a persistent feature. We compare the resulting (vertex-type) landscape of the MZ chain with the (face-type) landscape containing the Heisenberg XXX and Haldane--Shastry chains. We find that the landscapes only share a single point: the rational Haldane-Shastry chain. Using wrapping we show that the SZ chain is the antiperiodic 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.

Note: 37 pages, 3 figures, 1 table

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Contributing Institute(s):

1. Theorie-Gruppe (T)

Research Program(s):

1. 611 - Fundamental Particles and Forces (POF4-611) (POF4-611)
2. BrokenSymmetries - Exact Results from Broken Symmetries (101044226) (101044226)

Experiment(s):

1. No specific instrument

Appears in the scientific report 2024

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Database coverage:

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