Nonlocal dynamical correlations of strongly interacting electron systems

TLDR

The authors extend the dynamical mean‑field approximation to systematically include nonlocal corrections while preserving its causal properties and generality. They map the problem onto a self‑consistently embedded cluster and apply the scheme to the Falicov‑Kimball model with varying cluster sizes. The method recovers the exact DMFA in the single‑site limit, preserves sum rules, yields positive‑definite spectra, and demonstrates that nonlocal correlations suppress the charge‑density‑wave transition temperature.

Abstract

We introduce an extension of the dynamical mean-field approximation (DMFA) that retains the causal properties and generality of the DMFA, but allows for systematic inclusion of nonlocal corrections. Our technique maps the problem to a self-consistently embedded cluster. The DMFA (exact result) is recovered as the cluster size goes to 1 (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 nonlocal correlations suppress the charge-density wave transition temperature.