“…To compare the Bose-Hubbard system with the GOE case, we will compare the coefficients of Bose-Hubbard eigenstates with the Gaussian distribution with mean 0 and variance 1/D. It has been observed that mid-spectrum eigenstates of chaotic/ergodic many-body systems generally have coefficients with a near-Gaussian distribution [54,[74][75][76][77][78][79][80][81][82], in accord with Berry's conjecture [83]. On the other hand, eigenstates of integrable or many-body-localized systems, as well as eigenstates at the spectral edges of nominally chaotic systems, typically have markedly non-Gaussian distributions [74,75,78,84].…”