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Entanglement entropy under a particle bipartition provides complementaryinformation to mode entanglement as it is sensitive to interactions andparticle statistics at leading order and does not depend on any externallyimposed length scale. In this paper, we investigate the particle entanglemententropy in a system of $N$ interacting spinless lattice fermions in one spatialdimension by combining bosonization techniques with exact and approximatenumerical methods. We introduce a general scaling form for the fermionicparticle entanglement entropy captured by a shape function that enters as aextensive interaction induced correction to a known free fermion result. Ageneral asymptotic expansion in the total number of particles demonstrates thatits form is robust for different values of the R\'enyi index and highlights howquantum correlations are encoded in the $n$-particle density matrix of a puremany-body quantum state.

A Scaling Function for the Particle Entanglement Entropy of Fermions