Correlation Effects in the Moshinsky Model

Abstract

We investigate quantum correlations in the ground state of the Moshinsky model formed by N harmonically interacting particles confined in a harmonic potential. The model is solvable which allows an exact determination of entanglement between the subset of p particles and the remaining N − p particles. We study linear entropies and von Neumann entropies of the bipartitions and compare their behavior with that of the relative correlation energy and of the statistical Kutzelnigg coefficient.

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

“…In particular, a few attempts have been made recently towards understanding the entanglement in systems of interacting particles. For example, some light has been shed on entanglement both in quantum dot systems [6][7][8][9][10][11][12][13][14][15] and in systems of harmonically interacting particles in a harmonic trap (the so-called Moshinsky atom) [16][17][18][19][20][21][22][23]. Special attention has also been paid to the study of entanglement in the helium atoms and helium ions [24][25][26][27][28][29][30][31][32].…”

“…The reason for this lies in the fact that in most cases the determination of the wavefunction of a few-body state requires performing numerical calculations, which is a major problem in general. According to our best knowledge, the only N particle system of which the entanglement properties have been fully explored so far is the Moshinsky model system [17,18] The model on which we focus here is a system composed of N particles interacting via a long-range inverse power-law potential, which are confined by an external one-dimensional (1D) harmonic potential…”

Statistical Correlations of the N-particle Moshinsky Model

“…The entropies in this system can be solved exactly, helping us investigate correlations and test the entropic uncertainty principle of two subsystems containing arbitrary numbers of particles. Several topics about the correlation of Moshinsky model, such as the statistical and quantum correlation of the two-electron Moshinsky model [2][3][4], three-electron Moshinsky model and applying a uniform magnetic field in the two-electron model [5], and the quantum correlation in N-particle Moshinsky model [6], have been studied recently. In our present work, we focus on three topics: understanding statistical correlations, testing the entropic uncertainty principle, and comparing the statistical correlation to the quantum correlation of an N-particle Moshinsky model.…”

“…For a bipartite pure state, von Neumann entropy is half of the quantum mutual information [28]; therefore it can also be a good measure of quantum correlation. The eigenvalue structure of N-particle Moshinsky model has been studied in [29], and results of von Neumann entropy have been given by [6]. Shannon entropy does not equal to von Neumann entropy most of time.…”

Quantum Entanglement of Two Harmonically Trapped Dipolar Particles

“…Particularly the research activity has expanded towards investigating the entanglement properties in various systems composed of interacting particles. For instance, the recent studies include model systems such as the Moshinsky atom [17][18][19][20][21][22], helium atoms and helium-like atoms [23][24][25][26], quantum dot systems [27][28][29][30], and 1D systems of atoms interacting via a short-range contact interaction [31][32][33]. For details concerning the recent progress in entanglement studies of quantum composite systems, see [34].…”