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Generalization of the Hartree-Fock-Bogoliubov theory: one and two quasiparticle excitations

Paolo Tommasini·E. J. V. de Passos·M. O. C. Pires·A. F. R. de Toledo Piza
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Abstract

We present a generalization of the Hartree-Fock Bogoliubov (HFB) theory in which the coupling between one and two quasi-particles is taken into account.This is done by writing the excitation operators as linear combinations of one and two HFB quasi-particles. The excitation energies and the quasi-particle amplitudes are given by generalized Bogoliubov equations. The excitation spectrum has two branches. The first one is a discrete branch which is gapless and has a phonon character at large wave-length and, contrarily to HFB, is always stable. This branch is detached from a continuum branch whose threshold, at fixed total momentum, coincides with the two quasi-particle threshold of the HFB theory. The gap between these two branches at P=0 is equal to two times the HFB gap, which then provides for the relevant energy scale. We also give numerical results for a specific case.

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Paolo Tommasini, E. J. V. de Passos, M. O. C. Pires, A. F. R. de Toledo Piza. 2003-07-30. Generalization of the Hartree-Fock-Bogoliubov theory: one and two quasiparticle excitations. https://arxiv.org/abs/cond-mat/0307745

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