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Physical review. B, Condensed matter

Reply to “Comment on ‘Single-particle Green functions in exactly solvable models of Bose and Fermi liquids’ ”

Girish S. Setlur, Yia-Chung Chang

Published Sep 15, 1999• 2 citations
Publisher

Abstract

It is shown that the sea-boson model given in G.S. Setlur and Y.C. Chang, Phys. Rev. B 57, 15 144 (1998), is capable of reproducing the four-point correlation functions of fermion operators within the random-phase approximation, although an explicit expression for the sea-boson operator is still lacking.
DOI
10.1103/physrevb.60.8390

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Comment on “Single-particle Green functions in exactly solvable models of Bose and Fermi liquids”

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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.
This is a comment on the work of Kolomeisky et al., Phys. Rev. Lett. 85, 1146 (2000). We point out that they are using the wrong form of the energy functional for one-dimensional fermions. We point out two possible forms of the energy functional, both of which can be derived from first principles but using different methods. One is obtained from the collective field theory method, while the other is derived from the extended Thomas-Fermi method. These two forms of the energy functional do not support the soliton solutions which are obtained by Kolomeisky et al.
In a recent Letter (Phys. Rev. lett. 105, 195301 (2010)), Song et al. introduced a new variational approach to treat strong attractive boson-fermion (BF) correlations in BF atomic mixtures. The proposed theory predicts a first order phase transition to a condensate of composite BF pairs with center of mass momentum Q=0 as opposed to a composite fermionic molecular Fermi gas. We show in this comment that their approach is incorrect and moreover, by resorting to an exactly solvable model we demonstrate that there cannot be more than one correlated Q=0 BF pair in complete contradiction with their conclusions.