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

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