Determine whether deformed elliptic spin chains can be obtained via wrapping

Ascertain whether both the face-type and vertex-type elliptic long-range spin chains at the deformed level (including q-deformed and twisted versions) can be constructed by wrapping procedures analogous to the undeformed periodic and antiperiodic wrapping that reconstruct the Inozemtsev and SZ′ chains from the rational Haldane–Shastry chain.

Background

At the undeformed level, the authors show that wrapping the rational Haldane–Shastry chain with periodic boundary conditions yields the trigonometric Haldane–Shastry chain and, via Wick rotation and re-periodisation, the elliptic Inozemtsev chain; antiperiodic wrapping analogously yields the Fukui–Kawakami chain and the SZ′ chain.

They note that, while analogous boundary conditions persist (suitably q-deformed and twisted) at the deformed level, it is unclear whether similar wrapping constructions apply to obtain the full deformed elliptic landscapes for both the face and vertex sides.