A Unified Theory of Dynamical Mean Field and Spin Fluctuations

TL;DR

This paper introduces a unified theoretical framework combining dynamical mean field theory and spin fluctuation theory, capturing non-Fermi liquid behavior at quantum critical points in strongly correlated electron systems.

Contribution

It develops a new approach that integrates DMFT and SCR theory, incorporating spin fluctuations into DMFT as a $O(1/d)$ correction, applicable to quantum critical phenomena.

Findings

Demonstrates non-Fermi liquid behavior at QCP in Hubbard model

Recovers DMFT when spin fluctuations are ignored

Matches SCR theory predictions at quantum critical points

Abstract

A new approach is proposed which encompasses the dynamical mean field theory (DMFT) for strongly correlated electron systems and the self-consistent renormalization (SCR) theory of spin fluctuations. The latter is incorporated into DMFT as a $O(1/d)$ correction, where $d$ is the spatial dimensionality, but in a phenomenological way. The DMFT is completely recovered when the effect of spin fluctuation is omitted, whereas the properties at the quantum critical point (QCP) is the same as the SCR theory. An example of calculation is presented for the single band Hubbard model and the non-Fermi liquid behavior is demonstrated at QCP.