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).