Comment on "Robustness of a Local Fermi Liquid against Ferromagnetism and Phase Separation"

TL;DR

This paper critically examines the Local Fermi Liquid Theory in infinite dimensions, highlighting overlooked aspects such as vertex function k-dependence, Fermi surface anisotropy, and phase separation conditions.

Contribution

It clarifies key properties of the theory in infinite dimensions that were not fully addressed in previous work by Engelbrecht and Bedell.

Findings

Emphasizes the importance of k-dependence of the irreducible vertex function.

Highlights the anisotropy of the Fermi surface in the theory.

Discusses the necessary conditions for phase separation.

Abstract

In this paper we comment on the "Local Fermi Liquid Theory", proposed by Engelbrecht and Bedell [1]. We emphasize several important properties of the limit of infinite dimensions, in particular the k-dependence of the irreducible vertex function, the anisotropy of the Fermi surface and the necessary conditions for phase separation. It appears that these issues have not been fully appreciated in Ref. [1].