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We investigate the phase diagram of hard-core bosons in two-leg ladders inthe presence of soft-shoulder potentials. We show how the competition betweenlocal and non-local terms gives rise to a phase diagram with liquid phases withdominant cluster, spin-, and density-wave quasi-long-range ordering. Thesephases are separated by Berezinskii-Kosterlitz-Thouless, Gaussian, andsupersymmetric (SUSY) quantum critical transitions. For the latter, we providea phenomenological description of coupled SUSY conformal field theories, whosepredictions are confirmed by matrix-product state simulations. Our results aremotivated by, and directly relevant to, recent experiments with Rydberg-dressedatoms in optical lattices, where ladder dynamics has already been demonstrated,and emphasize the capabilities of these setups to investigate exotic quantumphenomena such as cluster liquids and coupled SUSY conformal field theories.

Phase diagram of Rydberg-dressed atoms on two-leg square ladders: Coupling supersymmetric conformal field theories on the lattice