Universality class of the $Z3$ ordering transition in Rydberg chains
In plain words
Rydberg chains can order with one excitation every third atom. The transition into this order may belong to an unusual chiral class or pass through an intermediate floating phase.
Precise statement
$1\mathrm{D}$ Rydberg chain with blockade covering two neighbours; the transition from disorder to $\mathrm{Z}3$ order. Determine whether it is direct and chiral (correlation exponent $\nu$ and dynamical exponent $z != 1$), passes through a floating incommensurate phase, or is in the 3-state Potts class at a special point. Answer: phase diagram and exponents along the boundary.
What would settle it
Large-scale DMRG with finite-size scaling of the full $1/r^{6}$ Hamiltonian, confirmed by Kibble-Zurek measurements across the boundary.
Status in the literature
Kibble-Zurek data (Keesling et al., Nature 2019) and numerical studies disagree on where the floating phase begins.
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