The self-energy problem in ground state and phonon calculation of quantum solids

Abstract

What part self-energy plays in T-matrix theories for quantum crystals has not yet been entirely understood. In particular, quantities related to the self-energy (e.g., the single-particle potential and the T matrix as an effective interaction extracted from the ground-state theory) have been used in phonon calculations in an uncritical fashion. In order to have a common basis for the comparison of the existing theories, we have diagrammatically reformulated the theories of Iwamoto and Namaizawa and of Guyer and Zane respectively. We then show what kind of approximations have been made in the existing theories concerning the single-particle potential and the effective interaction. Using the self-energy we propose an improved method to determine these quantities which enables us to treat phonon and ground-state calculations on an equal footing. Additionally, we set up a diagrammatic two-particle approximation method, which can be used in ground-state theory, and in phonon calculations as well. Contrary to the existing theories not referring to the self-energy, our procedure remains consistent, transferring the ground-state effective interaction to the phonon calculation. We show for example, that a suitably chosen effective interaction can be used as a renormalized interaction in an RPA calculation without overcounting any diagrams.