Fluctuations analysis of the spin susceptibility: N\'eel ordering revisited in dynamical mean field theory

TL;DR

This paper investigates how local fluctuations within dynamical mean field theory influence the Néel transition temperature in the Hubbard model, revealing that vertex screening enhances the transition temperature beyond simple approximations.

Contribution

It provides a detailed fluctuation analysis of the Néel temperature in the Hubbard model within DMFT, highlighting the contrasting effects of local moment formation on one- and two-particle correlations.

Findings

Vertex screening enhances $T_N$ beyond RPA predictions.

DMFT suppresses $T_N$ due to incoherence from the self-energy.

Local moment formation has opposite effects on different correlation functions.

Abstract

In this paper, we revisit the antiferromagnetic (AF) phase diagram of the single-band three-dimensional half-filled Hubbard model on a simple cubic lattice studied within the dynamical mean field theory (DMFT). Although this problem has been investigated extensively in the literature, a comprehensive understanding of the impact of the different one- and, in particular, two-particle local correlation functions of DMFT on the AF transition temperature is still missing. We have, hence, performed a fluctuation analysis of $T_N$ with respect to different local bosonic fluctuations (charge, spin, particle-particle) contained in the two-particle vertex of DMFT. Our results indicate that, beyond weak coupling, the screening of the DMFT vertex by local fluctuations leads to an enhancement of $T_N$ with respect to a random phase approximation (RPA) like calculation where this vertex is replaced by the bare interaction. The overall suppression of $T_N$ in DMFT with respect to RPA is then solely due to the incoherence introduced by the DMFT self-energy in the one-particle Green's functions. This illustrates the Janus-faced role of the local moment formation in the DMFT solution of the Hubbard model, which leads to completely opposite effects in the one- and two-particle correlation functions.