Typical Entanglement Entropy in Systems with Particle Number Conservation

The bipartite entanglement entropy is a measure of quantum correlations and is conjectured to be a probe of quantum chaos when computed for random eigenstates of a physical Hamiltonian. We derive the entanglement entropy of random states with a fixed particle number in any system of indistinguishable particles including fermions, bosons, spin systems and mixtures thereof. Remarkably, we are able to determine all terms up to constant order, notably that the leading term scales with the volume of the subsystem and that the constant term is universal. We numerically compute the entanglement entropy of typical eigenstates of the spin-XXZ and Bose-Hubbard models and show it agrees with our result at leading order whenever model parameters are in the quantum chaotic regime, thereby providing further support of the aforementioned conjecture.