Supersolid Order from Disorder: Hard-Core Bosons on the Triangular Lattice

We study the interplay of Mott localization, geometric frustration, and superfluidity for hard-core bosons with nearest-neighbor repulsion on the triangular lattice. For this model at half filling, we demonstrate that superfluidity survives for arbitrarily large repulsion, and that diagonal solid order emerges in the strongly correlated regime from an order-by-disorder mechanism. This is thus an unusual example of a stable supersolid phase of hard-core lattice bosons at a commensurate filling.

Figure 1

(a) Ground state superfluid density, calculated with exact diagonalization, quantum Monte Carlo, and variational wave function, with $J_{\perp }=1$. The inset is ${\rho }_s$ in the limit $J_z\to \infty$, calculated by ED (for several system sizes $N$) and VWF (in the thermodynamic limit). (b) The diagonal order parameter squared. Examples of the QMC extrapolations to $N\to \infty$ are illustrated in Fig. 2.

Figure 2

Finite-size scaling of QMC data for ${\rho }_s$ (a) and $⟨m{⟩}^2=S({\mathbf{k}}_0)/L^2$ (b). Here, $J_{\perp }=1$ and the inverse temperature is $\beta =10$. Error bars (illustrated) are much smaller than the symbol sizes. Dotted lines show linear extrapolations for the five largest system sizes. The thick solid (blue) line is a fit to $⟨m{⟩}^2\propto 1/L^2$.