Entanglement in helium

Benenti, Giuliano; Siccardi, Stefano; Strini, G.

doi:10.1140/epjd/e2013-40080-y

Cited by 45 publications

(96 citation statements)

References 43 publications

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“…This has been possible because for these harmonic systems we have been able to calculate analytically not only the one-body reduced matrix for bosons and fermions, but also the von Neumann entropy in the bosonic case as well as the linear entropy in the fermionic case. In doing so, we complement and extend to harmonic systems with an arbitrary number of particles the study of entanglement recently done for various two-electron models [13,[21][22][23][24][25] as well as some helium-like systems [6,14,15,17] and certain quantum complex networks [49].…”

Section: Discussionmentioning

confidence: 99%

Entanglement in N-harmonium: bosons and fermions

Benavides-Riveros¹,

Toranzo²,

Dehesa³

2014

J. Phys. B: At. Mol. Opt. Phys.

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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.

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Section: Discussionmentioning

confidence: 99%

Entanglement in N-harmonium: bosons and fermions

Benavides-Riveros¹,

Toranzo²,

Dehesa³

2014

J. Phys. B: At. Mol. Opt. Phys.

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“…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 effect of the confinement on the entanglement in the ground state of the helium atom has also been discussed in the literature [33].…”

Section: Introductionmentioning

confidence: 99%

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

Kościk

2015

Physics Letters A

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We study one-dimensional systems of N particles in a one-dimensional harmonic trap with an inverse power law interaction ∼ |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 = 1 (charged particles) and with d = 3 (dipolar particles).

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“…The amount of entanglement of the ground state and of the first few excited states of helium was assessed by using high-quality state-of-the-art wavefunctions [17]. Benenti et al [18] used a configuration-interaction variational method to compute the von Neumann and the linear entropy for several low-energy singlet and triplet eigenstates of helium. Lin et al [19] computed the spatial quantum entanglement of helium-like ions by means of spline techniques.…”

Section: Introductionmentioning

confidence: 99%

Magnetic alteration of entanglement in two-electron quantum dots

Simonović

Nazmitdinov

2015

Phys. Rev. A

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Quantum entanglement is analyzed thoroughly in the case of the ground and lowest states of two-electron axially symmetric quantum dots under a perpendicular magnetic field. The individualparticle and the center-of-mass representations are used to study the entanglement variation at the transition from interacting to noninteracting particle regimes. The mechanism of symmetry breaking due to the interaction, that results in the states with symmetries related to the later representation only, being entangled even at the vanishing interaction, is discussed. The analytical expression for the entanglement measure based on the linear entropy is derived in the limit of noninteracting electrons. It reproduces remarkably well the numerical results for the lowest states with the magnetic quantum number M ≥ 2 in the interacting regime. It is found that the entanglement of the ground state is a discontinuous function of the field strength. A method to estimate the entanglement of the ground state, characterized by the quantum number M , with the aid of the magnetic field dependence of the addition energy is proposed.

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Entanglement in helium

Cited by 45 publications

References 43 publications

Entanglement in N-harmonium: bosons and fermions

Entanglement in N-harmonium: bosons and fermions

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

Magnetic alteration of entanglement in two-electron quantum dots

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