Fig. 4: Statistics of the gap ratios of the spectrum of the entanglement Hamiltonian.

a Time evolution of the average gap ratio averaged over 6 randomly-drawn initial states and all symmetry sectors. The horizontal lines represent the averages for non-repulsive (Poisson, blue dotted) and repulsive (GUE, red dashed) distributions. Error bars indicate the standard deviation of the mean over the initial states and the symmetry superselection sectors of the reduced density matrix (see the Methods section). b Distribution of the entanglement-spectrum gap ratios, combined across 6 randomly-drawn initial states, all symmetry sectors, and all times in each of the regimes Early (E), Intermediate (I), and Late (L). A total of 840, 504, and 336 gaps are quantum-computed based on 10⁶ total shots, and their average is shown in orange. Simulated Bisognano-Wichmann results in the limit of infinite measurements are shown in cyan, and the exact predicted distributions in black. Blue-dotted and red-dashed curves represent Poisson and GUE distributions.