  Motivated by a recent inelastic neutron scattering experiment on
$\mathrm{YbMgGaO}_4$ \cite{William2019}, we reinvestigate the homogeneous spin
model on the triangular lattice. Using the cluster mean-field theory, we study
the phase diagram and the magnetic-field-induced phase transition. We find that
the phase boundary between the stripe state and the $120^{\circ}$
antiferromagnetic state is broadened by the magnetic field, leading to a
field-induced phase transition. This phase transition is suppressed by the
next-nearest neighbor exchange interaction $J_2/J_1$ and vanishes as
$J_2/J_1>0.13$. We find a parameter space at $J_2/J_1=0.1$, in which the
field-induce transition can be achieved and the deviation of theoretical spin
excitation energies from experimental data is only $5.4\%$. Our results imply
that an effective homogeneous spin model still works in $\mathrm{YbMgGaO}_4$.
