Fig. 2: Level statistics of the model.

a \(\left\{{q}_{\alpha }\right\}\)-averaged level spacing ratio as a function of the coupling strength parameter J/w. We truncate each spectrum to the \(k=\min (1000,{{{\mathcal{N}}}}/3)\) states with energies closest to the peak in the density of states, or an approximation thereof for system size N = 18, where \({{{\mathcal{N}}}}\) is the Hilbert space dimension. We also show the Poisson and Gaussian Orthogonal Ensemble (GOE) values as dashed and dotted black lines, respectively. The narrow localization-like plateau appears at around J/w ~ 1.5. b Distribution of the level spacing ratio across different charge sectors for fixed J/w = 5. The average values are also shown as vertical dotted lines (with uncertainties shown by the shaded regions), and the black dashed line indicates the Poisson value. While the distributions clearly shift towards Poisson as N increases, there is considerable weight at sub-Poisson values. The inset shows the trend in the \(\left\{{q}_{\alpha }\right\}\)-averaged value with 1/N, showing that it likely reaches Poisson in the thermodynamic limit. [We use all charge sectors for N = 8, 10, 1000 for N = 12, 14, 18, and 250 for N = 16. Uncertainties in all panels are calculated as the standard uncertainty in the mean.].