Momentum-Space Cluster Dual Fermion Method

TL;DR

This paper introduces an exact cluster dual fermion method that combines short-range and long-range correlation treatments, improving convergence and accuracy in non-perturbative regimes of many-body systems.

Contribution

The paper presents a novel, exact cluster dual fermion approach that avoids coarse graining errors, enhancing the treatment of correlations in dynamical mean field theory extensions.

Findings

Method converges to exact results regardless of cluster size

Improves accuracy of self-energy calculations

Demonstrates effectiveness with second-order approximation results

Abstract

Recent years have seen the development of two types of non-local extensions to the single-site dynamical mean field theory. On one hand, cluster approximations, such as the dynamical cluster approximation, recover short-range momentum-dependent correlations non-perturbatively. On the other hand, diagrammatic extensions, such as the dual fermion theory, recover long ranged corrections perturbatively. The correct treatment of both strong short-ranged and weak long-ranged correlations within the same framework is therefore expected to lead to a quick convergence of results, and offers the potential of obtaining smooth self-energies in non-perturbative regimes of phase space. In this paper, we present an exact cluster dual fermion method based on an expansion around the dynamical cluster approximation. Unlike previous formulations, our method does not employ a coarse graining approximation to the interaction, which we show to be the leading source of error at high temperature, and converges to the exact result independent of the size of the underlying cluster. We illustrate the power of the method with results for the second-order cluster dual fermion approximation to the single-particle self-energies and double occupancies.