Two-particle-correlations in a functional renormalization group scheme using a dynamical mean-field theory approach

TL;DR

This paper introduces a hybrid renormalization group scheme integrated with dynamical mean-field theory to efficiently compute two-particle correlations in lattice Hubbard models, capturing metallic, insulating, and short-range magnetic phases.

Contribution

It presents a novel hybrid scheme combining functional renormalization group with DMFT, enabling cost-effective calculation of two-particle vertices in complex correlated systems.

Findings

Successfully reproduces metallic and insulating phases in Hubbard models.

Calculates local and non-local two-particle vertices including magnetic fluctuations.

Analyzes frequency structures of vertices and compares single-site and cluster solutions.

Abstract

We apply a recently introduced hybridization-flow functional renormalization group scheme for Anderson-like impurity models as an impurity solver in a dynamical mean-field theory (DMFT) approach to lattice Hubbard models. We present how this scheme is capable of reproducing metallic and insulating solutions of the lattice model. Our setup also offers a numerically rather inexpensive method to calculate two-particle correlation functions. For the paramagnetic Hubbard-model on the Bethe lattice in infinite dimensions we calculate the local two-particle-vertex for the metallic and the insulating phase. Then we go to a two-site cluster-DMFT-scheme for the two-dimensional Hubbard-model that includes short-range antiferromagnetic fluctuations and obtain the local and non-local two-particle-vertex-functions. We discuss the rich frequency structures of these vertices and compare with the vertex in the single-site solution.