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

Abstract

Numerically exact quantum dynamics for indistinguishable particles: The multilayer multiconfiguration timedependent Hartree theory in second quantization representation Extensions of representations of the CAR algebra to the Cuntz algebra O 2 -the Fock and the infinite wedgeIn 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. C 2014 AIP Publishing LLC. [http://dx.

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