Operational entanglement of interacting spinless fermions in one-dimension

For indistinguishable itinerant particles subject to a super-selection rule fixing their total number, a portion of the spatial entanglement entropy in the ground state may be due solely to particle number fluctuations in the subregion and thus be inaccessible as a resource for quantum information processing. Excluding these contributions, we quantify the remaining operational entanglement in the t - V model of interacting spinless fermions in one spatial dimension via exact diagonalization. We find that it vanishes at the first order phase transition between a Tomonaga-Luttinger liquid and phase separated solid for attractive interactions and is maximal at the transition to the charge density wave for repulsive interactions. By examining the effects of filling fraction and partition size we explore the usefulness of the operational entanglement as a probe of quantum critical behavior.