Emergent Rokhsar-Kivelson point in realistic quantum Ising models

We show that the Rokhsar-Kivelson (RK) point in quantum dimer models (QDM) can emerge in realistic quantum Ising spin systems. Specifically, we investigate the $J_1$-$J_2$-$J_3$ transverse field Ising model on the triangular lattice with large-scale quantum Monte Carlo simulations. We find that the multicritical point in the phase diagram corresponds to the RK point of the QDM on the honeycomb lattice. We further measure the spectral functions and identify three branches of quadratic dispersions. In the phase diagram, we also find a sequence of incommensurate states, which meet the microscopic ingredients for the 'Cantor deconfinement' scenario. Our study provides a promising direction to realise the RK deconfinement in experimental platforms such as magnetic materials or programmable Rydberg arrays.