Exactly solvable topological phase transition in a quantum dimer model

Abstract: We introduce 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 then focus on a quantum dimer model on the triangular lattice, with doubly-periodic edge weights. For simplicity we consider a $2\times1$ periodic model in which all weights are set to one except for a tunable horizontal edge weight labeled $α$. We analytically show that the model exhibits a continuous quantum phase transition at $α=3$, changing from a topological $\mathbb{Z}_2$ quantum spin liquid ($α<3$) to a columnar ordered state ($α>3$). The dimer-dimer correlator decays exponentially on both sides of the transition with the correlation length $ξ\propto1/|α-3|$ 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. We explain the constant vison correlator in terms of loops 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.