Phase diagram of Rydberg-dressed atoms on two-leg triangular ladders

Dressed Rydberg atoms in optical lattices are a promising platform for the quantum simulation of intriguing phenomena emerging in strongly interacting systems. Relevant to such a setup, we investigate the phase diagram of hard-core bosons in a triangular ladder with next-to-nearest-neighbor interaction along each leg and nearest-neighbor interactions without hopping between the legs. For weak interactions, Abelian bosonization predicts a spin density wave and a fully gapless Luttinger liquid phase. Such liquids transition to a "spin-locked" cluster Luttinger liquid at strong interactions along each leg, as predicted by cluster bosonization. Interestingly, the competition with the zigzag interaction generates a charge density wave, a "polarized holonic" phase, and a crystalline phase at the filling 2/5, that we address via a semiclassical perturbative approach. Exact diagonaliza-tion and density matrix renormalization group simulations confirm the predictions and further characterize the phases and their transitions.