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000605573 005__ 20240529212811.0
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000605573 0247_ $$2arXiv$$aarXiv:2405.09718
000605573 0247_ $$2datacite_doi$$a10.3204/PUBDB-2024-01515
000605573 037__ $$aPUBDB-2024-01515
000605573 041__ $$aEnglish
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000605573 088__ $$2arXiv$$aarXiv:2405.09718
000605573 1001_ $$0P:(DE-HGF)0$$aKlabbers, Rob$$b0
000605573 245__ $$aLandscapes of integrable long-range spin chains
000605573 260__ $$c2024
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000605573 500__ $$a37 pages, 3 figures, 1 table
000605573 520__ $$aWe clarify how the elliptic integrable spin chain recently found by Matushko and Zotov (MZ) relates to various other known long-range spin chains. We evaluate various limits. More precisely, we tweak the MZ chain to allow for a short-range limit, and show it is the XX model with q-deformed antiperiodic boundary conditions. Taking $q\to 1$ gives the elliptic spin chain of Sechin and Zotov (SZ), whose trigonometric case is due to Fukui and Kawakami. It, too, can be adjusted to admit a short-range limit, which we demonstrate to be the antiperiodic XX model. By identifying the translation operator of the MZ chain, which is nontrivial, we show that antiperiodicity is a persistent feature. We compare the resulting (vertex-type) landscape of the MZ chain with the (face-type) landscape containing the Heisenberg XXX and Haldane--Shastry chains. We find that the landscapes only share a single point: the rational Haldane-Shastry chain. Using wrapping we show that the SZ chain is the antiperiodic version of the Inozemtsev chain in a precise sense, and expand both chains around their nearest-neighbour limits to facilitate their interpretations as long-range deformations.
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000605573 7001_ $$0P:(DE-H253)PIP1028527$$aLamers, Jules$$b1$$eCorresponding author$$udesy
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