Generalization of Lieb's variational principle to Bogoliubov–Hartree–Fock theory

Journal Article · Wed Jan 15 00:00:00 EST 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4853875· OSTI ID:22250854

Bach, Volker; Breteaux, Sébastien; Menge, Edmund ^[1]

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1. Technische Universität Braunschweig, Institut für Analysis und Algebra, Rebenring 31, 38106 Braunschweig (Germany)

In its original formulation, Lieb's variational principle holds for fermion systems with purely repulsive pair interactions. As a generalization we prove for both fermion and boson systems with semi-bounded Hamiltonian that the infimum of the energy over quasifree states coincides with the infimum over pure quasifree states. In particular, the Hamiltonian is not assumed to preserve the number of particles. To shed light on the relation between our result and the usual formulation of Lieb's variational principle in terms of one-particle density matrices, we also include a characterization of pure quasifree states by means of their generalized one-particle density matrices.

• OSTI ID: 22250854
• Journal Information: Journal of Mathematical Physics, Vol. 55, Issue 1; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOSONS
DENSITY MATRIX
FERMIONS
HAMILTONIANS
PAIRING INTERACTIONS
VARIATIONAL METHODS