Variational cluster approach to correlated electron systems in low dimensions

TL;DR

This paper introduces a generalized cluster method for correlated electron systems, unifying existing approaches like cluster-perturbation theory and cellular dynamical mean-field theory, and discusses its application to the 1D Hubbard model.

Contribution

It presents a unified variational cluster approach that encompasses previous methods as special cases, enhancing the analysis of low-dimensional correlated electron systems.

Findings

Unified framework for cluster approximations

Analysis of boundary conditions and cluster size effects

Application to the one-dimensional Hubbard model

Abstract

A self-energy-functional approach is applied to construct cluster approximations for correlated lattice models. It turns out that the cluster-perturbation theory (Senechal et al, PRL 84, 522 (2000)) and the cellular dynamical mean-field theory (Kotliar et al, PRL 87, 186401 (2001)) are limiting cases of a more general cluster method. Results for the one-dimensional Hubbard model are discussed with regard to boundary conditions, bath degrees of freedom and cluster size.