Lower bounds to the many-body problem using density matrices

L. J. Kijewski, J. K. Percus

Research output: Contribution to journalArticlepeer-review

Abstract

Variation principles for obtaining lower bounds by means of density matrices are applied to a number of many-body problems. This is done by means of restrictions derived from the study of exacly solvable models. Two classes of problems are considered: (a) obtaining a lower bound to the ground-state energy of a system of particles, and (b) obtaining a lower bound to the Helmholtz free energy. For the first case an exact lower bound is obtained for the ground-state energy of the particle-conserving Bogoliubov Hamiltonian. Of particular significance in the nonzero temperature case is a rigorous lower bound to the free energy of the Ising model with small external field at low temperatures.

Original languageEnglish (US)
Pages (from-to)228-234
Number of pages7
JournalPhysical Review
Volume164
Issue number1
DOIs
StatePublished - 1967

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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