Solids and Supersolids of Three-Body Interacting Polar Molecules on an Optical Lattice

We study the physics of cold polar molecules loaded into an optical lattice in the regime of strong three-body interactions, as put forward recently by Büchler et al. [Nature Phys. 3, 726 (2007)]. To this end, quantum Monte Carlo simulations, exact diagonalization, and a semiclassical approach are used to explore hard-core bosons on the 2D square lattice which interact solely by long-ranged three-body terms. The resulting phase diagram shows a sequence of solid and supersolid phases. Our findings are directly relevant for future experimental implementations and open a new route towards the discovery of a lattice supersolid phase in experiment.

Figure 1

Illustration of the leading 3B interactions $W_{ijk}$ with amplitude larger than 0.2, defining the minimal model studied here.

Figure 2

Central plot: Phase diagram of the minimal model obtained within the semiclassical approach as a function of the chemical potential $\mu$ and the nearest-neighbor hopping amplitude $t$. Gray (white) regions are SF (phase separated), and light (dark) blue denotes SSs (solids). Surrounding plots: schematic representation of the nature of some of the solid and SS phases. The greyscale of the circles represents the filling ($\mathrm{\text{white}}=\mathrm{\text{empty}}$, $\mathrm{\text{black}}=\mathrm{\text{full}}$), while the length and the direction of the red arrows denotes the amplitude and the phase of the SF component. The blue lines highlight the unit cell of the different structures.

Figure 3

Upper graph: density $n$ as a function of the chemical potential $\mu$ for the minimal model (cf. Fig. 1) at $t=0.5$ up to density $n=5/8$. Lower graph, upper panel: checkerboard order parameter $S(\pi ,\pi )/N$ from ED ($N=32$) and QMC ($N=12\times 12$) simulations. Lower panel: SF stiffness ${\rho }_s$ and condensate fraction ${\rho }_0$ obtained by QMC. Inset: ${\rho }_s$ at fixed $\beta =20$ and $\mu =15$ for $L=6,8,\dots ,16$.

Figure 4

Phase diagram obtained by SCA for different values of $t$ including all 3B terms with amplitudes $W_{ijk}>0.001$. Gray regions are SF, and light (dark) blue denotes SSs (solids), which were already present in the minimal model, cf. Fig. 2. The white regions encompass phase separation and further solids and SSs.