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A generalization of Lieb's variational principle

Sebastien Breteaux
Analysis Seminar
Thursday, 30 May, 2013, at 16:15, in Aud. D3 (1531-215)

The ground state energy, that is, the infimum of the energy over all possible states, is one of the most important quantities in quantum chemistry. Computing this energy in many-particle systems is a complex, if not impossible, task and, therefore, it is necessary to resort to approximation methods. In the Hartree-Fock approximation the infimum is calculated over a subclass of states called Slater determinants. To compute this infimum (in the fermionic case), Lieb's variational principle is a fundamental tool. It states that the infimum over Slater determinants equals the infimum over a subclass of quasifree states, which is easier to analyze.

We present a generalization of Lieb's variational principle for the Bogolubov-Hartree-Fock approximation. We prove that the infimum over pure quasifree states (which include the Slater determinants) equals the infimum over quasifree states.

Our result holds for a more general class of Hamiltonians than Lieb's variational principle and the method can be applied to both fermions and bosons.

Contact person: Bent Ørsted