A Unified Approach to Strong Local Correlations and Collective Fluctuations: Eliminating Divergence in the Spin Channel

TL;DR

This paper introduces fluctuating dynamical mean-field theory (fDMFT), an extension of DMFT that incorporates collective fluctuations to better capture long-range correlations and eliminate divergences in the spin channel.

Contribution

The paper proposes a novel fDMFT approach that includes collective fluctuations via functional integration, improving the accuracy of local correlation modeling in lattice systems.

Findings

fDMFT outperforms other diagrammatic extensions in the Hubbard model

Minimal fDMFT already provides accurate results

Diagrammatic corrections offer minor improvements

Abstract

Dynamical mean-field theory (DMFT) provides an optimal local approximation for correlated lattice systems by mapping the lattice onto a self-consistent effective impurity model. To account for the missing long-range correlations, we propose a novel extended approach, which we term fluctuating dynamical mean-field theory (fDMFT). It incorporates collective fluctuations of auxiliary impurity models across different sites via functional integration. Technically, this method involves obtaining a family of DMFT solutions on a grid for a self-consistent auxiliary classical field applied to the lattice. While the result can, in principle, be improved diagrammatically, we find that the minimal version of the theory already yields accurate results, with lowest-order diagrammatic corrections offering only minor improvements. This consistent framework, based on our fluctuating local field concept, demonstrates superior performance for the nearly half-filled Hubbard model compared to other known diagrammatic extensions of DMFT.