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arXiv · 1408.2150

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·Hartmut Hafermann
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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. 2014-12-29. Beyond extended dynamical mean-field theory: Dual boson approach to the two-dimensional extended Hubbard model. https://doi.org/10.1103/physrevb.90.235135

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