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We study the spin-1/2 XXZ model on the triangular lattice with a nearestneighbor 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, weobtain the variational phase diagram of this model on large lattices forarbitrary $J_z$ and either sign of $J_\perp$. For $J_\perp<0$, we find a$\sqrt{3}\times\sqrt{3}$ supersolid for $J_z/|J_\perp| \gtrsim 4.7$, inexcellent agreement with quantum Monte Carlo data. For $J_\perp >0$, a distinct$\sqrt{3}\times\sqrt{3}$ supersolid is found to emerge for $J_z/J_\perp \geq1$. Both supersolids exhibit a spontaneous density deviation from half-filling.At $J_z/J_\perp=\infty$, the crystalline order parameters of these twosupersolids are nearly identical, consistent with exact results.

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