  We investigate the chaotic phase of the Bose-Hubbard model [L. Pausch et al,
Phys. Rev. Lett. 126, 150601 (2021)] in relation to the bosonic embedded random
matrix ensemble, which mirrors the dominant few-body nature of many-particle
interactions, and hence the Fock space sparsity of quantum many-body systems.
The energy dependence of the chaotic regime is well described by the bosonic
embedded ensemble, which also reproduces the Bose-Hubbard chaotic eigenvector
features, quantified by the expectation value and eigenstate-to-eigenstate
fluctuations of fractal dimensions. Despite this agreement, in terms of the
fractal dimension distribution, these two models depart from each other and
from the Gaussian orthogonal ensemble as Hilbert space grows. These results
provide further evidence of a way to discriminate among different many-body
Hamiltonians in the chaotic regime.
