Phase Separation and Flux Quantization in the Doped Quantum Dimer Model on Square and Triangular Lattices

The doped two-dimensional quantum dimer model is investigated by numerical techniques on the square and triangular lattices, with significantly different results. On the square lattice, at small enough doping, there is always a phase separation between an insulating valence-bond solid and a uniform superfluid phase, whereas on the triangular lattice, doping leads directly to a uniform superfluid in a large portion of the resonating-valence-bond (RVB) phase. Under an applied Aharonov-Bohm flux, the superfluid exhibits quantization in terms of half-flux quanta, consistent with $Q=2e$ elementary charge quanta in transport properties.

Figure 1

Schematic phase diagrams for the triangular and the square lattice.

Figure 2

Slope of energy density [Eq. (2)] vs doping for different sizes. (a) Triangular lattice. (b) Square lattice.

Figure 3

Scaling of the critical doping $x_c$ defined by Maxwell construction with the inverse total number of sites. (a) Triangular lattice. (b) Square lattice.

Figure 4

Phase separation boundaries for the square and triangular lattices in the thermodynamic limit. The dashed lines correspond to the approximate location of the phase transition between plaquette and columnar phases [10] for the square lattice and between plaquette and RVB phases [8, 21] for the triangular lattice.

Figure 5

(a) First Brillouin zone. (b) Momentum dependence of the squared order parameter for the 196-site cluster ($14\times 14$). (c) Squared order parameter at the $M$ point as a function of the hole concentration $x$ and for different cluster sizes. The thermodynamic limit is depicted as a dashed line, with the corresponding error bar (see main text).

Figure 6

Energy spectrum vs (reduced) Aharonov-Bohm flux $\xi$, for a $4\times 4$ cluster with 4 holes at $v=0.70$ and $t=1.00$. (a) Torus geometry. Arbitrary BC are used in the transverse direction to obtain a continuous set of momenta leading to a continuum (shaded area). (b) The two low-energy branches for the case of a cylinder (dashed line) and including a small bond disorder (solid line).