Generic Mixed Columnar-Plaquette Phases in Rokhsar-Kivelson Models

We revisit the phase diagram of Rokhsar-Kivelson models, which are used in fields such as superconductivity, frustrated magnetism, cold bosons, and the physics of Josephson junction arrays. From an extended height effective theory, we show that one of two simple generic phase diagrams contains a mixed phase that interpolates continuously between columnar and plaquette states. For the square lattice quantum dimer model we present evidence from exact diagonalization and Green’s function Monte Carlo techniques that this scenario is realized, by combining an analysis of the excitation gaps of different symmetry sectors with information on plaquette structure factors. This presents a natural framework for resolving the disagreement between previous studies.

Figure 1

Schematic representation of the different ordered states considered, the columnar, the mixed columnar-plaquette, and the plaquette states. Dashed lines show the extra bonds of the checkerboard lattice of the equivalent hard-core boson model (see Ref. 2). On the left, dimers (thick bonds) map to bosons [circles (red online)].

Figure 2

First gap excitations. (a) Comparison between ED and GFMC methods for the $8\times 8$-site cluster for the interesting $q$ points. Size scaling of the gaps for the ($K$, $A_1$) (b) and ($\Gamma$, $B_1$) (c) symmetries.

Figure 3

(a) Behavior of the structure factor for the $8\times 8$-site cluster at $v/t=0.2$, along the path of the Brillouin zone depicted in the inset. A clear peak appears at point $K$. Size scaling of the order parameters in the two symmetry sectors are given, for ($K$, $A_1$) (b) and ($\Gamma$, $B_1$) (c).

Figure 4

Thermoynamic limit of the order parameters [solid lines (black and red online)] and of the first excitation gaps [dashed lines (blue and green online)] in function of $v/t$. $M_{A_1}(K)$ is multiplied by a factor 5 for clarity. A zoom around $v/t=0.6$ is shown in the inset. $M_{A_1}(K)$ is not multiplied here.