Shell-Filling Effect in the Entanglement Entropies of Spinful Fermions

We consider the von Neumann and Renyi entropies of the one-dimensional quarter-filled Hubbard model. We observe that for periodic boundary conditions the entropies exhibit an unexpected dependence on system size: for L = 4 mod 8 the results are in agreement with expectations based on conformal field theory, while for L = 0 mod 8 additional contributions arise. We explain this observation in terms of a shell-filling effect and develop a conformal field theory approach to calculate the extra term in the entropies. Similar shell-filling effects in entanglement entropies are expected to be present in higher dimensions and for other multicomponent systems.