Phys Rev Lett. 2026 Jul 31;137(5):056503. doi: 10.1103/gdd1-mxy3.
ABSTRACT
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 2×1 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 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∝1/|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, 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 ∞ (topological min-entropy) changes from log2 for the quantum spin liquid phase α<3, to 0 for the ordered phase α>3, thereby analytically confirming the topological nature of the phase transition.
PMID:42606476 | DOI:10.1103/gdd1-mxy3
