  For indistinguishable itinerant particles subject to a superselection rule
fixing their total number, a portion of the entanglement entropy under a
spatial bipartition of the ground state is due to particle fluctuations between
subsystems and thus is inaccessible as a resource for quantum information
processing. We quantify the remaining operationally accessible entanglement in
a model of interacting spinless fermions on a one dimensional lattice via exact
diagonalization and the density matrix renormalization group. We find that the
accessible entanglement exactly 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. Throughout the phase diagram, we discuss the connection
between the accessible entanglement entropy and the variance of the probability
distribution describing intra-subregion particle number fluctuations.
