1998/10/05 by Girish S. Setlur, Yia-Chung Chang, Setlur, Girish S. +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Nuclear physics research studies #Rare-earth and actinide compounds #Spectral Theory in Mathematical Physics #Strongly Correlated Electrons (cond-mat.str-el) #cond-mat.str-el
paper · pdf · doi:10.48550/arxiv.cond-mat/9810043
3 pages, RevTex, N(k,k^{'}) is given explicitly
openalex publication_date 1998/10/05 · arxiv created 1998/10/28 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this article, we revisit the question of the validity of Hartree-Fock and random-phase approximations. We show that there is a connection between the two and while the RPA as it is known in much of the physics literature is of limited validity, there is a generalised sense in which the random phase approximation is of much wider applicability including to systems that do not possess Fermi surfaces. The main conclusion is that the Hartree-Fock approximation is a mean-field idea applied to the density operator, and the random-phase approximation is a mean-field idea applied to the number operator. The generalised RPA is used to compute single-particle properties such as momentum distribution and spectral functions. It is found that we have to go beyond the generalised RPA and include fluctuations in the momentum distribution in order to recover a nonzero imaginary part of the one-particle self energy, which is also explicitly computed, all this in any number of spatial dimensions and no bosonization is needed.