Extended Data Fig. 7: Extracting the quantum critical point.

a, The mean Rydberg excitation density \(\langle n\rangle \) versus detuning Δ/Ω on a 16 × 16 array. The data are fitted within a window (dashed lines) to a cubic polynomial (red curve) as a means of smoothing the data. b, The peak in the numerical derivative of the fitted data (red curve) corresponds to the critical point Δ_c/Ω = 1.12(4) (red shaded regions show uncertainty ranges, obtained from varying fit windows). In contrast, the point-by-point slope of the data (grey) is too noisy to be useful. c, Order parameter \(\mathop{ {\mathcal F} }\limits^{ \sim }({\rm{\pi }},{\rm{\pi }})\) for the chequerboard phase versus Δ/Ω measured on a 16 × 16 array with the value of the critical point from b superimposed (red line), showing the clear growth of the order parameter after the critical point. d, DMRG simulations of  \(\langle n\rangle \) versus Δ/Ω on a 10 × 10 array. For comparison against the experimental fitting procedure, the data from numerics are also fitted to a cubic polynomial within the indicated window (dashed lines). e, The point-by-point slope of the numerical data (blue curve) has a peak at Δ_c/Ω = 1.18 (blue dashed line), in good agreement with the results (red dashed line) from both the numerical derivative of the cubic fit on the same data (red curve) and the result of the experiment. f, DMRG simulation of \(\mathop{ {\mathcal F} }\limits^{ \sim }({\rm{\pi }},{\rm{\pi }})\) versus Δ/Ω, with the exact quantum critical point from numerics shown (red line).