Beyond extended dynamical mean-field theory: Dual boson approach to the two-dimensional extended Hubbard model

TL;DR

This paper develops and implements the dual boson approach to improve the extended dynamical mean-field theory for the two-dimensional extended Hubbard model, revealing significant effects of vertex corrections on phase boundaries.

Contribution

The paper introduces a numerical implementation of the dual boson approach for the extended Hubbard model, highlighting the importance of vertex corrections beyond EDMFT.

Findings

Diagrammatic corrections lower the charge-ordering phase boundary.

The approach bridges RPA and EDMFT regimes.

Vertex corrections are crucial even at small interactions.

Abstract

The dual boson approach [Ann. Phys. 327, 1320 (2012)] provides a means to construct a diagrammatic expansion around the extended dynamical mean-field theory (EDMFT). In this paper, we present the numerical implementation of the approach and apply it to the extended Hubbard model with nearest-neighbor interaction $V$. We calculate the EDMFT phase diagram and study the effect of diagrams beyond EDMFT on the transition to the charge-ordered phase. Including diagrammatic corrections to the EDMFT polarization shifts the EDMFT phase boundary to lower values of $V$. The approach interpolates between the random phase approximation in the weak coupling limit and EDMFT for strong coupling. Neglecting vertex corrections leads to results reminiscent of the EDMFT+$GW$ approximation. We however find significant deviations from the dual boson results already for small values of the interaction, emphasizing the crucial importance of fermion-boson vertex corrections.