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Physical Review C

Natural orbitals, overlap functions, and mean-field orbitals in an exactly solvableA-body system

Dimitri Van Neck, A.E.L. Dieperink, Michel Waroquier

Published May 1, 1996• 14 citations
Publisher

Abstract

We consider a simple but nontrivial many-body system interacting through short-range forces, and confirm a property of such systems that was recently proposed on general grounds, namely, that single-particle overlap functions, spectroscopic factors, and separation energies of the bound (A-1)-particle eigenstates can be derived from the one-body density matrix of the A-particle system in its ground state. The basis of natural orbitals for the system is constructed and its properties are discussed. We also investigate the high-momentum content of the bound-state overlap functions and momentum distribution. It is found that the mean field provides a good approximation for the bound-state overlap functions even in the region of large momenta, where the total momentum distribution is already enhanced by several orders of magnitude over the mean-field result. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevc.53.2231

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We consider a simple but nontrivial many-body system interacting through short-range forces, and confirm a property of such systems that was recently proposed on general grounds, namely, that single-particle overlap functions, spectroscopic factors, and separation energies of the bound (A-1)-particle eigenstates can be derived from the one-body density matrix of the A-particle system in its ground state. The basis of natural orbitals for the system is constructed and its properties are discussed. We also investigate the high-momentum content of the bound-state overlap functions and momentum distribution. It is found that the mean field provides a good approximation for the bound-state overlap functions even in the region of large momenta, where the total momentum distribution is already enhanced by several orders of magnitude over the mean-field result. \textcopyright{} 1996 The American Physical Society.
We consider an exactly solvable Hamiltonian for bosons in one-dimension interacting through zero-range attractive forces, and construct a complete basis of its A-particle eigenstates. The structure of the single-particle spectral function in the removal domain is investigated, by taking the overlap of the A-particle ground state with the various excited states of the $(A\ensuremath{-}1)$ system. In particular we study the contribution to the spectral function of the different break-up channels in the $A\ensuremath{-}1$ continuum, and compare the results to general statements available in the literature. It is shown that the asymptotic behavior in coordinate space does not agree with conventional assumptions. The relation to recent (e,e′p)(e,{e}^{'}p)(e,e′p) experiments at large values of missing energy and momentum is pointed out.
In this work we derive a systematic short-range expansion of the many-body wave function. At leading order, the wave function is factorized to a zero-energy s -wave correlated pair and spectator particles, while terms that include energy derivatives and larger orbital angular momentum two-body functions appear at subleading orders. The validity of the expansion is tested for the two-body case, as well as the many-body case, where infinite neutron matter is considered. An accurate and consistent description of both coordinate-space two-body densities and the one-body momentum distribution is obtained. These results show the possibility to utilize such an expansion for describing different observables in strongly-interacting many-body systems, including nuclear, atomic and condensed-matter systems. This work also opens the path for a systematic description of large momentum transfer reactions in nuclear systems sensitive to short-range correlations, provides a link between such experiments and low-energy nuclear physics, and motivates measurement of new observables in these experiments.
We analyze properties of trial wave functions in fractional quantum Hall effect, generated by the "short-range", three-body repulsion and its mean field approximation.Ground states of electron repulsion Hamiltonians at filing factor ν = 1/2 are evaluated as a description of physically observed state ν = 5/2.We analyze overlaps between the Moore-Read state and its mean field approximation for different number of particles and compare both states with ground state of the Coulomb interaction in the first excited Landau level.Our study also includes examination of electron-electron correlation functions and electron densities of excited states for both interactions.
We investigate the suitability of natural orbitals as a basis for describing many-body excitations. We analyze to which extent the natural orbitals describe both bound as well as ionized excited states and show that depending on the specifics of the excited state the ground-state natural orbitals may yield a good approximation. We show that the success of reduced density-matrix functional theory in describing molecular dissociation lies in the flexibility provided by fractional occupation numbers while the role of the natural orbitals is minor.
Abstract The natural and Dyson orbitals are studied for small helium drops comprising 5 to 20 helium atoms interacting via a soft two-body Gaussian potential. The wave functions of these drops have been obtained in the hyperspherical cluster model (HCM) which provides a correct description of the single-particle behavior at large separations from the system. The natural orbitals are obtained from diagonalization of the nonlocal one-body density matrix, while Dyson orbitals are constructed by the direct overlap of the wave functions of two drops differing by one boson. This overlap converges with an increasing basis of the HCM. The shapes and occupancies of the natural orbitals, as well as their link to Dyson overlap and evolution with increasing number of atoms, are discussed. Both natural and Dyson orbitals can be used to represent the density of the system. However, the natural orbital representation is demonstrated to be superior. With increasing boson numbers the difference between Dyson and natural orbitals becomes less prominent and is expected to disappear in infinitely large systems of identical bosons.
We introduce an energy functional for ground-state electronic structure calculations. Its variables are the natural spin-orbitals of singlet many-body wave functions and their joint occupation probabilities deriving from controlled approximations to the two-particle density matrix that yield algebraic scaling in general, and Hartree-Fock scaling in its seniority-zero version. Results from the latter version for small molecular systems are compared with those of highly accurate quantum-chemical computations. The energies lie above full configuration interaction calculations, close to doubly occupied configuration interaction calculations. Their accuracy is considerably greater than that obtained from current density-functional theory approximations and from current functionals of the one-particle density matrix.