## 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 language | English (US) |
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Pages (from-to) | 228-234 |

Number of pages | 7 |

Journal | Physical Review |

Volume | 164 |

Issue number | 1 |

DOIs | |

State | Published - 1967 |

## ASJC Scopus subject areas

- Physics and Astronomy(all)