Identification of an RVB liquid phase in a quantum dimer model with competing kinetic terms

Starting from the mean-field solution of a spin-orbital model of $\mathrm{Li}\mathrm{Ni}{\mathrm{O}}_2$, we derive an effective quantum dimer model (QDM) that lives on the triangular lattice and contains kinetic terms acting on four-site plaquettes and six-site loops. Using exact diagonalizations and Green’s function Monte Carlo simulations, we show that the competition between these kinetic terms leads to a resonating valence bond (RVB) state for a finite range of parameters. We also show that this RVB phase is connected to the RVB phase identified in the Rokhsar-Kivelson model on the same lattice in the context of a generalized model that contains both the six-site loops and a nearest-neighbor dimer repulsion. These results suggest that the occurrence of an RVB phase is a generic feature of QDM with competing interactions.

Figure 1

Example of type-A (left) and type-B (right) clusters with 16 and 12 sites, respectively.

Figure 2

(Color online) Difference between $E_{00}$ and $E_{11}$, the total ground-state energies of the topological sectors with $p=q=0$ and $p=q=1$, respectively. The results are found by exact diagonalizations for clusters with 12 and 36 sites.

Figure 3

(Color online) Dimer-dimer correlations on the 36-site cluster. The dimer of reference is the thickest one in the up-right corner. The thicker the line, the farther the value of the correlation from the uniform distribution equal value $1∕36$. Solid lines are used when the correlation is higher than $1∕36$, and dashed lines when it is lower.

Figure 4

(Color online) Topological gaps for $V∕t=0$ as a function of $1∕\sqrt{N}$, where $N$ is the number of sites and for different values of $t^{\prime }∕t$. Upper panel: Small values of $t^{\prime }∕t$, where the gap opens for large clusters. Lower panel: Larger values of $t^{\prime }∕t$. For $t^{\prime }∕t\gtrsim 1.6$, the finite-size gap closes upon increasing the cluster size, signaling a liquid phase.

Figure 5

(Color online) Dimer-dimer correlation function for a 108-site cluster along a horizontal line as a function of the distance for $t^{\prime }∕t=2$ and $V∕t=0$. The dashed line corresponds to $1∕36$, the value in the absence of correlations.

Figure 6

(Color online) Topological gap for $t^{\prime }∕t=1$ and for various $V∕t$ as a function of $1∕\sqrt{N}$, where $N$ is the number of sites. Small and large values of $V∕t$ have been shown separately in the upper and lower panels for clarity.

Figure 7

(Color online) Phase diagram in the $t^{\prime }\text{−}V$ plane. A wide disordered region extends all the way from the standard QDM ($t^{\prime }∕t=0$ axis) to the purely kinetic QDM ($V∕t=0$ axis). The description of the symbols is given in the text.

Figure 8

Sign convention for a triangle.

Figure 9

A four-dimer loop.

Figure 10

The three types of six-dimer loops.