  We investigate the phase diagrams of the effective spin models derived from
Fermi-Hubbard and Bose-Hubbard models with Rashba spin-orbit coupling, using
string bond states, one of the quantum tensor network states methods. We focus
on the role of quantum fluctuation effect in stabilizing the exotic spin phases
in these models. For boson systems, and when the ratio between inter-particle
and intra-particle interaction $\lambda > 1$, the out-of-plane ferromagnetic
(FM) and antiferromagnetic (AFM) phases obtained from quantum simulations are
the same to those obtained from classic model. However, the quantum
order-by-disorder effect reduces the classical in-plane XY-FM and XY-vortex
phases to the quantum X/Y-FM and X/Y-stripe phase when $\lambda < 1$. The
spiral phase and skyrmion phase can be realized in the presence of quantum
fluctuation. For the Fermi-Hubbard model, the quantum fluctuation energies are
always important in the whole parameter regime. %, which are much larger than
those of the Bose model. A general picture to understand the phase diagrams
from symmetry point of view is also presented.
