Emergent Z₂ phase transition in the magnetization plateau.

We study the phase diagram of Rydberg ladders having n = 2, 3 legs in the presence of both staggered and uniform detuning with amplitudes Δ and λ respectively. We show that these ladders host a plateau with fixed Rydberg excitation density 1/(2 n) for a wide range of λ/Δ. Our analysis further unravels the existence of an emergent quantum phase transition stabilized via an order-by-disorder mechanism inside the plateau. This transition belongs to the Ising (three-state Potts) universality class for ladders with n = 2(3) legs. We identify the competing terms responsible for this transition and estimate the critical detuning as λ_c/Δ = (n − 1) / (n + 1), which agrees well with exact-diagonalization based numerical studies. We also study the fate of this transition for a realistic interaction potential, which allows for the possibility of direct verification of this transition in standard experiments.