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

Erik G. C. P. van Loon , Alexander I. Lichtenstein , Mikhail I. Katsnelson , Olivier Parcollet (1) , Hartmut Hafermann

1 SPhT - Service de Physique Théorique

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.

Domaines: Autre [cond-mat.other]

Erik G. C. P. van Loon, Alexander I. Lichtenstein, Mikhail I. Katsnelson, Olivier Parcollet, Hartmut Hafermann. Beyond extended dynamical mean-field theory: dual boson approach to the two-dimensional extended Hubbard model. 2014. ⟨cea-01058818⟩