Extended Data Fig. 8: Scaling properties of the center SLIOM in the largest symmetry sector.

a, Full-width-half-maxima σ of the center SLIOM distributions over the system size N, evaluated for system sizes ranging from N = 90 to N = 450. The number of clusters in the largest symmetry sector does not necessarily increase with every increment in the system size, explaining the sawtooth feature in the plot that becomes less prominent for larger N. The fractional width is observed to scale with an exponent α = 0.49, in agreement with our results in the main text. b, A scaling collapse of center SLIOM distributions shows that their width indeed appears to scale as \(\sqrt{N}\). The site index i is plotted such that the center site on the chain of particles corresponds to i = 0. Each curve has a jagged feature between half-integer sites and integer sites, leading to separated Bell-shaped distributions.