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Journal of Physics A Mathematical and General

Derivation of energy lower bound models for translation-invariant many-fermion systems

R J M Carr

Published Feb 1, 1978• 5 citations
Publisher

Abstract

A derivation of the SHRIMP energy lower bound model for translation-invariant many-fermion systems is given. Previous models are obtained as special cases.
DOI
10.1088/0305-4470/11/2/008

Related papers

On the paper by RJM Carr: 'derivation of energy lower bound models for translation-invariant many-fermion systems'

E. B. Balbutsev

A detailed derivation of the energy lower bound model (SHRIMP model) for a translation-invariant many-fermion system has recently been proposed (Carr 1978). The author asserts that an N-particle shell model retaining antisymmetry in all N particles is obtained. The present author wishes to point out the error in this derivation which makes the SHRIMP model wrong leaving correct the related RIP and HIP models.

Journal of Physics A Mathematical and General•Jul 1, 1978•1 citation

Many-particle systems. IX. RIP and SHRIMP models

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For pt.VIII see ibid., vol.4, p.665 (1971). The energy lower bound models HIP and SHIP may be substantially improved for small numbers of fermions by a simple modification to the limiting procedure in their derivation. It is shown that for intermediate values of N the modified SHIP model gives in some cases the best available lower bounds.

Journal of Physics A Mathematical and General•Apr 1, 1977•7 citations

Incorrect lower bounds for the N-fermion problem

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The symmetrised versions of the Carr (1978) and Post (1977) lower bounds for N-fermion systems are examined. It is shown that both formulae, known also as the SHIP and SHRIMP models, are incorrectly derived.

Journal of Physics A Mathematical and General•Jul 1, 1978•1 citation

Energy lower bounds for translation-invariantN-fermion systems

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A restriction on the choice of translation-invariant coordinates for a system of N identical fermions, interacting by pair forces, allows a lower bound to be established on the ground-state binding energy. This bound is the sum of the first N -1 eigenvalues of a two-particle problem. The quality of the method is found to depend on the choice of coordinates consistent with the initial restraint, the optimum set giving a bound which, in the case of Hooke's law pair forces, is [radical]3( N -1)/2( N +1) times the exact energy.

Proceedings of the Physical Society•May 1, 1967•32 citations

Lower energy bounds for quantum lattice Hamiltonians

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We derive general lower energy bounds for the ground state energy of any translationally invariant quantum lattice Hamiltonian. The bounds are given by the ground state energy of renormalized Hamiltonians on finite clusters.

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F. David Peat

Certain lower bounds to the ground state energy of N-fermion systems have been derived in the literature using the properties of reduced density matrices.It is indicated that while some good approximations to the energy may be obtained by similar consideration the rigorous lower bound expressions lie too far below the exact energy to prove generally useful.

Canadian Journal of Physics•Jan 15, 1970•4 citations
A restriction on the choice of translation-invariant coordinates for a system of N identical fermions, interacting by pair forces, allows a lower bound to be established on the ground-state binding energy. This bound is the sum of the first N -1 eigenvalues of a two-particle problem. The quality of the method is found to depend on the choice of coordinates consistent with the initial restraint, the optimum set giving a bound which, in the case of Hooke's law pair forces, is [radical]3( N -1)/2( N +1) times the exact energy.