Improved bounds on many-body hamiltonians

Francisco Machado, Dominic V. Else, Chetan Nayak +1 more

Achour Benslama, Abboud Metatla, A. Bachkhaznadji +5 more

D. Boosé, J. Richert

Minoru Harada

The ground-state energy of the Lipkin, Meshkov, and Glick many-body Hamiltonian as determined by the Brueckner theory is shown to be an upper bound on the exact value for 2, 3, 4, 6, and 8 particles. Improved upper bounds are obtained for 2, 4, 6, and 8 particles by taking one half of the usually adopted hole-state potential. This latter result lends support to Tobocman's early conjecture about the choice of the self-consistent single-particle potential.

Calvin M. Johnson

Martin Manning

Lower bound energy formulae for the N-fermion problem of the type used by Hall (1967) and Post (1956) are considered in terms of a reduced density operator for the interparticle separation. In bounds of this type the N-body energy is bounded below by a sum of eigen-energies of states of relative motion weighted by occupations for the relative states. It is shown that the wavefunctions of relative motion are subject to constraints and in particular must be zero when the particle separation is zero. This modifies the energy spectrum of the reduced Hamiltonian of relative motion and improves the lower bound due to Hall. The improvement is demonstrated for some simple model problems. Furthermore it is shown that the bounds of this type currently known do not exhibit saturation regardless of the interaction details. This leads to some speculation on improved lower bounds.