Quantum entanglement in many-body quantum systems on a lattice is an indicator for quantum chaos or quantum integrability. We use the bipartite entanglement entropy as a measure for quantum entanglement using the von Neumann formula. We examine highly excited eigenstates of the Bose-Hubbard model in the quantum chaotic regime. We calculate the eigenstates via exact diagonalization of the Hamiltonian. For deriving an analytical expression for the average entanglement entropy we use random matrix theory. Because of the presence of the global symmetry U(1), the Bose-Hubbard model conserves the total particle number. Hence, we need canonical random states and to decompose the Hilbert space into sectors with a fixed particle number. I examined bosons with a cut-off for the local occupation numbers and bosons without a cut-off. I introduced a new way of determining the leading term of the canonical average entanglement entropy for bosons on a lattice from the mean-field approximation of the grand canonical entanglement entropy. The average entanglement entropy of highly excited eigenstates of the Bose-Hubbard model with parameters t = U = 1 is in agreement with the analytical solution from random matrix theory.
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