Unusual Liquid State of Hard-Core Bosons on the Pyrochlore Lattice

We study the physics of hard-core bosons with unfrustrated hopping ($t$) and nearest-neighbor repulsion ($V$) on the three dimensional pyrochlore lattice. At half-filling, we demonstrate that the small $V/t$ superfluid state eventually becomes unstable at large enough $V/t$ to an unusual insulating state which displays no broken lattice translation symmetry. Equal time and static density correlators in this insulator are well described by a mapping to electric field correlators in the Coulomb phase of a $U(1)$ lattice gauge theory, allowing us to identify this insulator with a $U(1)$ fractionalized Mott-insulating state. The possibility of observing this phase in suitably designed atom-trap experiments with ultracold atoms is also discussed, as are specific experimental signatures.

Figure 1

(a) Pyrochlore lattice and the underlying diamond lattice. (b) Ring-exchange process on plaquettes of the diamond lattice.

Figure 2

(a) Superfluid density at $\beta =30$—the break around $V=19.2$ indicates observed hysteresis near the (weakly) first-order transition. (b) Schematic phase diagram: dots with error bars denote observed transitions, and dot at (19.4,1/30) denotes location at which insulating phase data is displayed in Figs. 3, 4.

Figure 3

Static $S^{\alpha \alpha }(\mathbf{q},{\omega }_n=0)$ and equal time $C^{\alpha \alpha }(\mathbf{q},\tau =0)$ correlators of the density in the deconfined phase for $\beta =30$, $V=19.4$. The lines are a fit to the predictions of noncompact $U(1)$ gauge theory on the diamond lattice as discussed in the text, with fit parameters displayed above.

Figure 4

(a) The same values of $\sqrt{\kappa \gamma }$ and ${ϵ}^2\sqrt{\kappa /\gamma }$ (displayed in the legend) fit data at different temperatures for fixed $V/t$. (b) $S^{\alpha \alpha }(\mathbf{q},{\omega }_n=0)$ and $\beta C^{\alpha \alpha }(\mathbf{q},\tau =0)$ for $V=19.4$ are essentially equal at $\beta =1$, but not at $\beta =30$.