The von Neumann entanglement entropy for Wigner-crystal states in one dimensional N-particle systems

•We study confined systems of N particles with an inverse power law interaction.•We apply the harmonic approximation to the systems.•We derive closed form expressions for the asymptotic von Neumann entropy.•The asymptotic von Neumann entropy grows monotonically as N increases.

We study one-dimensional systems of N   particles in a one-dimensional harmonic trap with an inverse power law interaction ∼|x|−d∼|x|−d. Within the framework of the harmonic approximation we derive, in the strong interaction limit, the Schmidt decomposition of the one-particle reduced density matrix and investigate the nature of the degeneracy appearing in its spectrum. Furthermore, the ground-state asymptotic occupancies and their natural orbitals are derived in closed analytic form, which enables their easy determination for a wide range of values of N. A closed form asymptotic expression for the von Neumann entanglement entropy is also provided and its dependence on N   is discussed for the systems with d=1d=1 (charged particles) and with d=3d=3 (dipolar particles).