Mott physics and spin fluctuations: a unified framework

TL;DR

This paper introduces a unified formalism for strongly correlated electron systems that captures the transition from weak to strong coupling, revealing Mott physics and spin fluctuations through a self-consistent vertex approach.

Contribution

It develops a local approximation of the dynamical three-leg vertex, self-consistently computed with a quantum impurity model, bridging spin-fluctuation and atomic limits.

Findings

The vertex becomes strongly frequency-dependent near the Mott transition.

Enhanced spin fluctuations lead to momentum-dependent self-energy at low temperatures.

Doping results in Fermi arcs, indicating pseudo-gap behavior.

Abstract

We present a formalism for strongly correlated electrons systems which consists in a local approximation of the dynamical three-leg interaction vertex. This vertex is self-consistently computed with a quantum impurity model with dynamical interactions in the charge and spin channels, similar to dynamical mean field theory (DMFT) approaches. The electronic self-energy and the polarization are both frequency and momentum dependent. The method interpolates between the spin-fluctuation or GW approximations at weak coupling and the atomic limit at strong coupling. We apply the formalism to the Hubbard model on a two-dimensional square lattice and show that as interactions are increased towards the Mott insulating state, the local vertex acquires a strong frequency dependence, driving the system to a Mott transition, while at low enough temperatures the momentum-dependence of the self-energy is enhanced due to large spin fluctuations. Upon doping, we find a Fermi arc in the one-particle spectral function, which is one signature of the pseudo-gap state.