1999/11/15 by R. Chitra, Gabriel Kotliar, G. Kotliar · 10 citations
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Bifurcation #Bifurcation theory #Dynamical systems theory #Functional equation #Lattice (music) #Mathematics #Nonlinear system #Partial differential equation #Physics #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum mechanics #Statistical physics #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.63.115110
published as Phys.Rev.B63:115110,2001 · 9 pages
arxiv created 1999/11/15 · openalex publication_date 2001/03/01 · arxiv updated 2016/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We construct a functional for the single-particle Green's function, which is a variant of the standard Baym-Kadanoff functional. The stability of the stationary solutions to the functional is directly related to aspects of the irreducible particle hole interaction through the Bethe-Salpeter equation. A startling aspect of this functional is that it allows a simple and rigorous derivation of both the standard and extended dynamical mean-field (DMFT) equations as stationary conditions. Though the DMFT equations were formerly obtained only in the limit of infinite lattice coordination, the functional described in the work presents a way of directly extending DMFT to finite-dimensional systems, both on a lattice and in a continuum. Instabilities of the stationary solution at the bifurcation point of the functional signal the appearance of a zero mode at the Mott transition which then couples to physical quantities resulting in divergences at the transition.