Real-space renormalized dynamical mean field theory

TL;DR

The paper introduces rr-DMFT, a method that enables large cluster calculations in dynamical mean field theory by decomposing clusters into smaller ones with real-space renormalization, accurately capturing spatial correlations.

Contribution

The paper presents a novel rr-DMFT approach that simplifies large cluster calculations in DMFT by incorporating real-space renormalization at the lowest order, improving accuracy over traditional small-cluster methods.

Findings

Successfully reproduces noninteracting and atomic limits.

Captures growth of antiferromagnetic correlations.

Accurately predicts the Mott transition critical point.

Abstract

We propose real-space renormalized dynamical mean field theory (rr-DMFT) to deal with large clusters in the framework of a cluster extension of the DMFT. In the rr-DMFT, large clusters are decomposed into multiple smaller clusters through a real-space renormalization. In this work, the renormalization effect is taken into account only at the lowest order with respect to the intercluster coupling, which nonetheless reproduces exactly both the noninteracting and atomic limits. Our method allows us large cluster-size calculations which are intractable with the conventional cluster extensions of the DMFT with impurity solvers, such as the continuous-time quantum Monte Carlo and exact diagonalization methods. We benchmark the rr-DMFT for the two-dimensional Hubbard model on a square lattice at and away from half filling, where the spatial correlations play important roles. Our results on the spin structure factor indicate that the growth of the antiferromagnetic spin correlation is taken into account beyond the decomposed cluster size. We also show that the self-energy obtained from the large-cluster solver is reproduced by our method better than the solution obtained directly for the smaller cluster. When applied to the Mott metal-insulator transition, the rr-DMFT is able to reproduce the reduced critical value for the Coulomb interaction comparable to the large cluster result.