Supersolidity in the triangular lattice spin-1/2 XXZ model: A variational perspective

We study the spin-1/2 XXZ model on the triangular lattice with a nearest neighbor antiferromagnetic Ising coupling $J_z>0$ and unfrustrated ($J_{\perp }<0$) or frustrated ($J_{\perp }>0$) kinetic terms in zero magnetic field. Incorporating long-range Jastrow correlations over a mean field spin state, we obtain the variational phase diagram of this model on large lattices for arbitrary $J_z$ and either sign of $J_{\perp }$. For $J_{\perp }<0$, we find a $\sqrt{3}\times \sqrt{3}$ supersolid for $J_z\mathrm{/}\mathrm{\mid }{J}_{\perp }\mathrm{\mid }\gtrsim 4.7$, in excellent agreement with quantum Monte Carlo data. For $J_{\perp }>0$, a distinct $\sqrt{3}\times \sqrt{3}$ supersolid is found to emerge for $J_z/J_\perp \geq 1$. Both supersolids exhibit a spontaneous density deviation from half-filling. At $J_z\mathrm{/}{J}_{\perp }=\mathrm{\infty }$, the crystalline order parameters of these two supersolids are nearly identical, consistent with exact results.