  We study the system of strongly interacting spinor bosons in a square lattice
subject to the isotropic Rashba SOC $ \alpha=\beta $. It supports collinear
spin-bond correlated magnetic Y-x phase, a gapped in-commensurate (IC-)
co-planar IC-XY-y phase, a non-coplanar commensurate (C-) $ 3 \times 3 $
Skyrmion crystal phase (SkX). The state at the Abelian point $
\alpha=\beta=\pi/2 $ is just an AFM state in a rotated basis. Slightly away
from the point, we identify a spurious $ U(1) $ symmetry, develop a novel and
non-perturbative method to calculate not only the gap, but also the excitation
spectrum due to the order from quantum disorder (OFQD) mechanism. We construct
a symmetry based effective action to investigate the quantum Lifshitz
transition from the Y-x state to the IC-XY-y state and establish the connection
between the phenomenological parameters in the effective action and those
evaluated by the microscopic non-perturbative OFQD analysis in the large $ S $
limits. Experimental implications on cold atoms and some 4d or 5d Kitaev
materials are discussed.
