Fluctuating field series: towards calculations of correlated systems with high accuracy

TL;DR

This paper presents a new regular series expansion method based on fluctuating local fields for accurately calculating properties of weakly- and moderately-correlated fermionic systems, outperforming some existing methods in certain regimes.

Contribution

The paper introduces a novel non-perturbative fluctuating local field approach for fermionic systems, suitable for medium-sized lattices and cluster approximations, with demonstrated convergence and accuracy.

Findings

Benchmarking against quantum Monte Carlo data shows good agreement.

Series expansion converges uniformly for susceptibility calculations.

Method is effective below the DMFT Néel temperature.

Abstract

We introduce regular series expansion for weakly- and moderately-correlated fermionic systems, based on Fluctuating Local Field approach. The method relies on the explicit account of leading fluctuating mode(s) and is therefore suitable for medium-sized lattices. It can be also used as a solver for the cluster approximations for infinite-size lattices. We introduce classical fluctuating field coupled to fermionic collective mode(s). This way, fluctuations in selected modes are treated in a non-perturbative way. Other degrees of freedom are accounted for the diagram expansion performed at each value of the fluctuating field. The method is benchmarked for the $U/t=1$ and $U/t=2$ Hubbard lattices at half-filling. Results for susceptibility in the antiferromagnetic channel along with the single particle density of states are compared with the numerically exact quantum Monte Carlo data. Calculations up to the third order of the series expansion are performed and show a uniform convergence to the reference result for the susceptibility. This convergence is observed well below the DMFT Ne\'el temperature and makes our practically simple method applicable in a much wider temperature range than DMFT-based diagrammatic schemes.