Optimal route to quantum chaos in the Bose-Hubbard Hamiltonian

The dependence of the chaotic phase of the Bose-Hubbard Hamiltonian [1,2] on particle number, system size and particle density is investigated in terms of spectral and eigenstate features. Within the energy and parameter range where chaos fully unfolds, the expectation value and the eigenstate-to-eigenstate fluctuations of the fractal dimensions of Bose-Hubbard eigenstates show clear signatures of ergodicity and are well described by random-matrix theory (RMT) [1,2]. As the limit of infinite Hilbert space dimension is approached along different directions, the fastest convergence to the random-matrix predictions is achieved at fixed particle density ≲ 1 [3]. Despite the agreement on the level of low-order statistical moments, the model is ever more distinguishable from RMT in terms of its full fractal dimension distributions as Hilbert space grows. These results provide evidence of a way to discriminate among different many-body Hamiltonians in the chaotic regime.
[1] L. Pausch et al., Phys. Rev. Lett. 126, 150601 (2021)
[2] L. Pausch et al., New J. Phys. 23, 123036 (2021)
[3] L. Pausch et al., J. Phys. A 55, 324002 (2022)