%0 Electronic Article
%A Klabbers, Rob
%A Lamers, Jules
%T Landscapes of integrable long-range spin chains
%N DESY-24-062
%M PUBDB-2024-01515
%M DESY-24-062
%M arXiv:2405.09718
%D 2024
%Z 37 pages, 3 figures, 1 table
%X 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→ 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.
%F PUB:(DE-HGF)25
%9 Preprint
%R 10.3204/PUBDB-2024-01515
%U https://bib-pubdb1.desy.de/record/605573