Effective-action approach to strongly correlated fermion systems

Abstract

We construct a new 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 new 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 new 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.

Fermi surfaces and gauge-gravity duality

“…In the evaluation of the free energy, such contributions are known as the Luttinger-Ward functional [28][29][30][31] …”

Extended variational cluster approximation for correlated systems

“…This issue has been discussed thouroughly in the context of EDMFT. 19,35,38 Here, a similar strategy can be taken to handle the ordered phase in EVCA. EVCA equations developed in Secs.…”

“…36 Here, besides the one-particle Green's function G, a certain two particle-Green's function Π should be chosen according to the form of the nonlocal interactions. For the construction of Φ [G, Π], we use a derivation that is formally different from that of Chitra et al, 35 but is more suitable for the present purpose. This is embodied, e.g., in that the universality of Φ [G, Π] and Ω [G, Π] is easily understood from the derivation process.…”

“…To extend the VCA, we first express the grand potential functional Ω [G, Π] by the generalized Luttinger-Ward functional Φ [G, Π]. 35 This is accomplished through a Legendre transformation. 36 Here, besides the one-particle Green's function G, a certain two particle-Green's function Π should be chosen according to the form of the nonlocal interactions.…”

Electronic Structure and Magnetic Properties of Solids

“…Realistic implementation of DMFT within electronic structure framework 88,89 can be viewed as a spectral density functional theory 90,91,92,93 . The central quantity of this method is the local Green functionĜ loc (r, r ′ , ω), which in the non-collinear version should be considered as the matrix in spin variableŝ…”