Cellular Dynamical Mean Field Theory for the 1D Extended Hubbard Model

TL;DR

This paper applies cellular dynamical mean field theory with exact diagonalization to the 1D Hubbard model, analyzing the Mott transition and convergence, and compares results with DMRG to evaluate accuracy.

Contribution

It develops and assesses a CDMFT approach using exact diagonalization for the 1D Hubbard model, focusing on convergence and resource optimization.

Findings

Successful application of CDMFT to 1D Hubbard model

Comparison shows good agreement with DMRG results

Insights into Mott transition and computational resource allocation

Abstract

We explore the use of exact diagonalization methods for solving the self consistent equations of the cellular dynamical mean field theory (CDMFT) for the one dimensional regular and extended Hubbard models. We investigate the nature of the Mott transition and convergence of the method as a function of cluster size as well as the optimal allocation of computational resources between bath and `cluster-impurity' sites, with a view to develop a renormalization group method in higher dimensions. We assess the performance of the method by comparing results for the Green's functions in both the spin density wave (SDW) and charge density wave (CDW) phases with accurate density matrix renormalization group (DMRG) calculations.