A Scaling Function for the Particle Entanglement Entropy of Fermions

TL;DR

This paper introduces a scaling function for particle entanglement entropy in interacting fermions, revealing how quantum correlations are encoded and providing a universal correction to free fermion results.

Contribution

It proposes a general scaling form for fermionic particle entanglement entropy using bosonization and numerical methods, highlighting a robust shape function for various parameters.

Findings

The shape function captures interaction effects as an extensive correction.

The scaling form is robust across different Rénnyi indices.

Quantum correlations are encoded in the n-particle density matrix.

Abstract

Entanglement entropy under a particle bipartition provides complementary information to mode entanglement as it is sensitive to interactions and particle statistics at leading order and does not depend on any externally imposed length scale. In this paper, we investigate the particle entanglement entropy in a system of $N$ interacting spinless lattice fermions in one spatial dimension by combining bosonization techniques with exact and approximate numerical methods. We introduce a general scaling form for the fermionic particle entanglement entropy captured by a shape function that enters as a extensive interaction induced correction to a known free fermion result. A general asymptotic expansion in the total number of particles demonstrates that its form is robust for different values of the R\'enyi index and highlights how quantum correlations are encoded in the $n$-particle density matrix of a pure many-body quantum state.