Doped singlet-pair crystal in the Hubbard model on the checkerboard lattice

In the limit of large nearest-neighbor and on-site Coulomb repulsions, the Hubbard model on the planar pyrochlore lattice maps, near quarter filling, onto a doped, quantum, fully packed loop model. The phase diagram exhibits at quarter filling a quantum state of matter, the resonating singlet-pair crystal, an insulating phase breaking lattice symmetry. Properties of a few doped holes or electrons are investigated. In contrast to the doped quantum antiferromagnet, phase separation is restricted to very small hopping, leaving an extended “window” for superconducting pairing. However, the latter is more fragile for large hopping than in the case of the antiferromagnet. The existence of a fermionic supersolid is discussed.

Figure 1

(Color online) Proposed phase diagram as a function of $W$ and $J$. See text for a description of the relevant phases.

Figure 2

(Color online) Energies of the 1/4 filled GS and singlet excited states characterized by different quantum numbers (as shown) vs $W$ for $J=0$ (a). Inset: energy differences with respect to GS. (b) Same data for excited states only, and finite values of $J$. Phase transitions (shown by vertical bars) are signaled by the crossing between excited states (left) and by a $W$-independent energy (right). The dashed line in (a) shows the $E^{\left(1\right)}$ perturbation result (see text).

Figure 3

(Color online) Single hole bandwidth (in units of $\mid t\mid$) as a function of $t_2∕\mid t\mid$ for a fixed (physical) ratio of $J∕t_2$. For comparison, the same quantity for the quantum AF on the square lattice is indicated, as a function of $J∕t$, by a dashed (blue) line.

Figure 4

(Color online) Two-hole $Z$ factor $Z_{2h}$ versus $t_2∕\mid t\mid$ for $J=0$ and $J∕t_2=0.5$. The case of two doped electrons is also shown $\left(Z_{2e}\right)$ as hashed symbols (for $J=0.5$). For comparison, the same quantity is shown as circles (blue online) for two holes doped into the quantum AF on the square lattice vs $J∕t$ [data for a 26-site cluster (Ref. 19)].

Figure 5

(Color online) Hole pair binding energy (in units of $t$) vs $t_2∕\mid t\mid$ for both signs of $t$. For comparison, the case of the doped quantum AF on the square lattice is shown (data for $N=26$) (Ref. 19).