Determine the magnetic order selected by the zero-field spin-1/2 Kitaev–Gamma model

Determine whether the zero-field spin-1/2 ferromagnetic Kitaev–positive-[?]Gamma model exhibits six-site period-three magnetic order or spiral order, as the cited 24-site exact-diagonalization study does not resolve this distinction.

Background

The paper studies the ferromagnetic Kitaev–Gamma model and finds that its static response softens near the period-three wave vector Q=2qM/3\bm Q=2\bm q_{\mathrm M}/3, consistent with magnetic ordering tendencies identified in classical and tensor-network studies. However, the authors note that a 24-site exact-diagonalization calculation identifies only a compatible threefold-degenerate sector and does not determine whether the underlying order is a six-site pattern or a spiral. Resolving this distinction is therefore an explicit unresolved question relevant to characterizing the magnetic instability of the spin-1/2 model.

References

For the spin-$1/2$ model in a field, a thermodynamic-limit iTPS calculation likewise stabilizes the corresponding six-site state, while zero-field 24-site exact diagonalization finds a compatible threefold-degenerate sector but does not resolve whether its order is six-site or spiral.

— Temperature evolution of spin dynamics in extended Kitaev models within an Abrikosov fermion theory beyond mean field  (2610.13401 - Sasamoto et al., 9 Oct 2026) in Section 4.2, subsection “Kitaev–Gamma model,” paragraph discussing the period-three ordering wave vector