Entanglement in N-harmonium: bosons and fermions

Abstract

The ground-state entanglement of a single particle of the N-harmonium system (i.e., a completely-integrable model of $N$ particles where both the confinement and the two-particle interaction are harmonic) is shown to be analytically determined in terms of $N$ and the relative interaction strength. For bosons, we compute the von Neumann entropy of the one-body reduced density matrix by using the corresponding natural occupation numbers. There exists a critical number $N_c$ of particles so that below it, for positive values of the coupling constant, the entanglement grows when the number of particles is increasing; the opposite occurs for $N>N_c$. For fermions, we compute the one-body reduced density matrix for the closed-shell spinned case. In the strong coupling regime, the linear entropy of the system decreases when $N$ is growing. For fixed $N$, the entanglement is found (a) to decrease (increase) for negatively (positively) increasing values of the coupling constant, and (b) to grow when the energy is increasing. Moreover, the spatial and spin contributions to the total entanglement are found to be of comparable size.

arXiv comment27 pages, 9 figures, minor changes, 4 improved figures, references added, some typos corrected

References in corpus (23)

• Quantum entanglement
• Area laws for the entanglement entropy - a review
• Entropy and Area
• Quantum Correlations in Two-Fermion Systems
• Entanglement entropy in fermionic Laughlin states
• Structure of Fermionic Density Matrices: Complete N-representability Conditions
• Essential entanglement for atomic and molecular physics
• Entanglement as Measure of Electron-Electron Correlation in Quantum Chemistry Calculations
• Pinning of Fermionic Occupation Numbers
• Separability Criteria and Entanglement Measures for Pure States of N Identical Fermions
• Entanglement in fermion systems and quantum metrology
• Three fermions with six single particle states can be entangled in two inequivalent ways
• On the criterion for Bose-Einstein condensation for particles in traps
• Entropy and Exact Matrix Product Representation of the Laughlin Wave Function
• Analytic Harmonic Approach to the N-body problem
• Entanglement in helium
• Natural Orbitals and Occupation Numbers for Harmonium: Fermions vs. Bosons
• Quantification of linear entropy for quantum entanglement in He, H- and Ps- ions using highly-correlated Hylleraas functions
• Density functional theory on phase space
• The lowest excited configuration of harmonium
• Quantum Statistics and Thermodynamics in the Harmonic Approximation
• Information sharing in Quantum Complex Networks
• Exact Eigenfunctions of $N$-Body system with Quadratic Pair Potential

Cited by in corpus (28)

• Entropic measures of Rydberg-like harmonic states
• Rényi entropies of the highly-excited states of multidimensional harmonic oscillators by use of strong Laguerre asymptotics
• Relating correlation measures: the importance of the energy gap
• Analytic solutions of topologically disjoint systems
• Pinning of Fermionic Occupation Numbers: General Concepts and One Dimension
• Variance of an anisotropic Bose-Einstein condensate
• Analysis of a trapped Bose-Einstein condensate in terms of position, momentum, and angular-momentum variance
• Heisenberg and entropic uncertainty measures for large-dimensional harmonic systems
• Solvable Model of a Generic Trapped Mixture of Interacting Bosons: Reduced Density Matrices and Proof of Bose-Einstein Condensation
• Solvable model of a generic driven mixture of trapped Bose-Einstein condensates and properties of a many-boson Floquet state at the limit of an infinite number of particles
• Detecting dimensional crossover and finite Hilbert space through entanglement entropies
• Long- and short-range interaction footprints in entanglement entropies of two-particle Wigner molecules in 2D quantum traps
• Bipartite correlations in quantum resonance states
• Quantum entanglement of two harmonically trapped dipolar particles
• Spatial entanglement of fermions in one-dimensional quantum dots
• Extracting Many-Body Quantum Resources within One-Body Reduced Density Matrix Functional Theory
• Effects Beyond Center-of-Mass Separability in a Trapped Bosonic Mixture: Exact Results
• Properties of a trapped multiple-species bosonic mixture at the infinite-particle-number limit: A solvable model
• Mode Entanglement in Fermionic and Bosonic Harmonium
• Entanglement and correlations in an exactly-solvable model of a Bose-Einstein condensate in a cavity
• Morphology of an interacting three-dimensional trapped Bose-Einstein condensate from many-particle variance anisotropy
• Fragmentation of a trapped bosonic mixture
• Quantum correlations in one-dimensional Wigner molecules
• Correlation Effects in a Trapped Bose-Fermi Mixture: Exact Results
• Fragmentation of a trapped multiple-species bosonic mixture
• Spatial correlations and entanglement in a hybrid system of N fermion pairs with harmonic interaction
• Single-particle-exact density functional theory
• Fragmentation of identical and distinguishable bosons' pairs and natural geminals of a trapped bosonic mixture