Reinvestigation of the homogeneous spin model in YbMgGaO${}_4$

Motivated by a recent inelastic neutron scattering experiment on ${\mathrm{Y}\mathrm{b}\mathrm{M}\mathrm{g}\mathrm{G}\mathrm{a}\mathrm{O}}_4$ \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 $J_2\mathrm{/}{J}_1$ and vanishes as $J_2\mathrm{/}{J}_1>0.13$. We find a parameter space at $J_2\mathrm{/}{J}_1=0.1$, in which the field-induce transition can be achieved and the deviation of theoretical spin excitation energies from experimental data is only $5.4\mathrm{\%}$. Our results imply that an effective homogeneous spin model still works in ${\mathrm{Y}\mathrm{b}\mathrm{M}\mathrm{g}\mathrm{G}\mathrm{a}\mathrm{O}}_4$.