Dual Boson Diagrammatic Monte Carlo Approach Applied to the Extended Hubbard Model

TL;DR

This paper introduces a numerically exact Dual Boson Diagrammatic Monte Carlo method for the extended Hubbard model, effectively capturing local and non-local electronic correlations and identifying phase transition points.

Contribution

It develops a novel Monte Carlo approach combining dynamical mean-field theory with diagrammatic techniques for the dual boson framework, enabling precise solutions at the two-particle vertex level.

Findings

Exact solutions for the self-energy in the extended Hubbard model.

Identification of regimes where ladder approximation is insufficient.

Estimation of the charge density wave transition point.

Abstract

In this work we introduce the Dual Boson Diagrammatic Monte Carlo technique for strongly interacting electronic systems. This method combines the strength of dynamical mean-filed theory for non-perturbative description of local correlations with the systematic account of non-local corrections in the Dual Boson theory by the diagrammatic Monte Carlo approach. It allows us to get a numerically exact solution of the dual boson theory at the two-particle local vertex level for the extended Hubbard model. We show that it can be efficiently applied to description of single particle observables in a wide range of interaction strengths. We compare our exact results for the self-energy with the ladder Dual Boson approach and determine a physical regime, where description of collective electronic effects requires more accurate consideration beyond the ladder approximation. Additionally, we find that the order-by-order analysis of the perturbative diagrammatic series for the single-particle Green's function allows to estimate the transition point to the charge density wave phase.