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

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.
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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. Physical Review B: Condensed Matter and Materials Physics, American Physical Society, 2014, 90 (235135), ⟨10.1103/PhysRevB.90.235135⟩. ⟨cea-01232753⟩

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