Numerical investigation of quantum phases and phase transitions in a two-leg ladder of Rydberg atoms

Abstract

Experiments on chains of Rydberg atoms appear as a playground to study quantum phase transitions in 1D. As a natural extension, we report a quantitative ground-state phase diagram of Rydberg atoms arranged in a two-leg ladder interacting via van der Waals potential. We address this problem numerically, using the density matrix renormalization group algorithm. Our results suggest that, quite remarkably, Z_{k} crystalline phases, with the exception of the checkerboard phase, appear in pairs characterized by the same pattern of occupied rungs but distinguishable by a spontaneously broken Z[over ̃]_{2} symmetry between the two legs of the ladder. Within each pair, the two phases are separated by a continuous transition in the Ising universality class, which eventually fuses with the Z_{k} transition, whose nature depends on k. According to our results, the transition into the Z_{2}⊗Z[over ̃]_{2} phase changes its nature multiple times, including an Ashkin-Teller transition that is surprisingly stable over an extended interval, followed by the Z_{4}-chiral transition, and finally in a two step-process mediated melting via the floating phase. The transition into the Z_{3} phase with resonant states on the rungs belongs to the three-state Potts universality class at the commensurate point, to the Z_{3}-chiral Huse-Fisher universality class away from it, and eventually it is through an intermediate floating phase. The Ising transition between Z_{3} and Z_{3}⊗Z[over ̃]_{2} phases, entering the floating phase, opens the possibility to realize lattice supersymmetry in Rydberg quantum simulators.