We consider a family of generalized Rokhsar-Kivelson (RK) Hamiltonians, which are reverse-engineered to have an arbitrary edge-weighted superposition of dimer coverings as their exact ground state at the RK point. We focus on a quantum dimer model on the triangular lattice, with doubly periodic edge weights. For simplicity we consider a $2\times 1$ periodic model in which all weights are set to one except for a tunable horizontal edge weight labeled $\alpha$. We analytically show that the model exhibits a continuous quantum phase transition at $\alpha =3$, changing from a topological ${\mathbb{Z}}_2$ quantum spin liquid ($\alpha <3$) to a columnar ordered state ($\alpha >3$). The dimer-dimer correlator decays exponentially on both sides of the transition with the correlation length $\xi \propto 1/|\alpha -3|$ and as a power-law at criticality. The vison correlator exhibits an exponential decay in the spin liquid phase, but becomes a constant in the ordered phase, which we explain in terms of loop statistics of the double-dimer model. Using finite-size scaling of the vison correlator, we extract critical exponents consistent with the 2D Ising universality class. Additionally, we analytically show that the topological Rényi entropy of order $\infty$ (topological min-entropy) changes from log2 for the quantum spin liquid phase $\alpha <3$, to 0 for the ordered phase $\alpha >3$, thereby analytically confirming the topological nature of the phase transition.

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• Quantum phase transitions
• Quantum spin liquid
• Topological phases of matter
• Strongly correlated systems
• Triangular lattice