Landscapes of integrable long-range spin chains
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. The limit 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.
Cite
@article{arxiv.2405.09718,
title = {Landscapes of integrable long-range spin chains},
author = {Rob Klabbers and Jules Lamers},
journal= {arXiv preprint arXiv:2405.09718},
year = {2025}
}
Comments
v1: 37 pages, 3 figures, 1 table. v2: 39 pages, 3 figures, 1 table; extended Sect 5.2 and App C, minor changes. v3 37 pages, 3 figures, 1 table; minor changes, added footnote 2