Nonlocal Dynamical Correlations of Strongly Interacting Electron Systems

TL;DR

This paper extends the dynamical mean field approximation to include non-local correlations by using self-consistently embedded clusters, improving the modeling of strongly interacting electron systems.

Contribution

It introduces a systematic method to incorporate non-local correlations into DMFA via cluster embedding, maintaining causality and generality.

Findings

Non-local correlations suppress the CDW transition temperature.

Sum rules are preserved in the extended method.

Spectra remain positive definite with non-local corrections.

Abstract

We introduce an extension of the dynamical mean field approximation (DMFA) which retains the causal properties and generality of the DMFA, but allows for systematic inclusion of non-local corrections. Our technique maps the problem to a self-consistently embedded cluster. The DMFA (exact result) is recovered as the cluster size goes to one (infinity). As a demonstration, we study the Falicov-Kimball model using a variety of cluster sizes. We show that the sum rules are preserved, the spectra are positive definite, and the non-local correlations suppress the CDW transition temperature. \