Perturbative calculation of non-local corrections to dynamical mean field theory

TL;DR

This paper develops a perturbative method to incorporate non-local corrections into dynamical mean-field theory (DMFT), providing a systematic way to improve its accuracy for strongly correlated electron systems in low dimensions.

Contribution

It introduces a perturbative technique based on the spatial damping of Green's functions, justifying and extending DMFT's applicability to finite-dimensional strongly correlated systems.

Findings

Accurately calculates the magnetic short-range order parameter in the Hubbard model.

Demonstrates excellent agreement with cluster approaches for non-local corrections.

Analyzes the impact of corrections on the local density of states.

Abstract

A technique allowing for a perturbative treatment of nonlocal corrections to the single-site dynamical mean-field theory (DMFT) in finite dimensions is developed. It is based on the observation that in the case of strong electron correlation the one-electron Green's function is strongly spatially damped so that its intersite matrix elements may be considered as small perturbations. Because the non-local corrections are at least quadratic in these matrix elements, DMFT in such cases may be a very accurate approximation in dimensions d = 1-3. This observation provides a rigorous justification for the application of DMFT to physical systems. Furthermore, the technique allows for a systematic evaluation of the nonlocal corrections. This is illustrated with the calculation of the magnetic short range order parameter for nearest neighbor spins in the half filled Hubbard model on the square lattice in its insulating phase which exhibits an excellent agreement with the results of a recent cluster approach.As a second example we study the lowest order correction to the DMFT self-energy and its influence on the local density of states.