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arXiv:1604.07734 · Physical review. B./Physical review. B

From local to nonlocal correlations: The Dual Boson perspective

E. A. Stepanov, A. Huber, Erik G. C. P. van Loon, Alexander I. Lichtenstein, Mikhail I. Katsnelson

Published Nov 7, 2016• 45 citations
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Abstract

Extended dynamical mean-field theory (EDMFT) is insufficient to describe nonlocal effects in strongly correlated systems, since corrections to the mean-field solution are generally large. We present an efficient scheme for the construction of diagrammatic extensions of EDMFT that avoids the usual double-counting problem by using an exact change of variables (the Dual Boson formalism) to distinguish the correlations included in the dynamical mean-field solution and those beyond. With a computational efficiency comparable to the $\mathrm{EDMFT}+\mathrm{GW}$ approach, our scheme significantly improves on the charge order transition phase boundary in the extended Hubbard model.

DOI
10.1103/physrevb.94.205110

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Extended dynamical mean-field theory (EDMFT) is insufficient to describe nonlocal effects in strongly correlated systems, since corrections to the mean-field solution are generally large. We present an efficient scheme for the construction of diagrammatic extensions of EDMFT that avoids the usual double-counting problem by using an exact change of variables (the Dual Boson formalism) to distinguish the correlations included in the dynamical mean-field solution and those beyond. With a computational efficiency comparable to the EDMFT+GW\mathrm{EDMFT}+\mathrm{GW}EDMFT+GW approach, our scheme significantly improves on the charge order transition phase boundary in the extended Hubbard model.
Extended dynamical mean-field theory (EDMFT) is insufficient to describe non-local effects in strongly correlated systems, since corrections to the mean-field solution are generally large. We present an efficient scheme for the construction of diagrammatic extensions of EDMFT that avoids usual double counting problem by using an exact change of variables (the dual boson formalism) to distinguish the correlations included in the mean-field solution and those beyond. With a computational efficiency comparable to EDMFT+GW approach, our scheme significantly improves on the charge order transition phase boundary in the extended Hubbard model.
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 nonperturbative description of local correlations with the systematic account of nonlocal 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 the 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.
We discuss the phase diagram of the extended Hubbard model with both attractive and repulsive local and nonlocal interactions. The extended dynamical mean-field theory (EDMFT) and the dual boson method (DB) are compared. The latter contains additional nonlocal correlation effects that are not incorporated in EDMFT. We find that EDMFT and DB give almost identical results in the attractive V regime, where phase separation occurs. This is quite a difference with the previously studied repulsive V regime, where EDMFT and DB give very different phase boundaries for the checkerboard order phase, especially at small U .
In electronic systems with long-range Coulomb interaction, the nonlocal Fock-exchange term has a band-widening effect. While this effect is included in combined many-body perturbation theory and dynamical mean field theory (DMFT) schemes, it is not taken into account in standard extended DMFT (EDMFT) calculations. Here, we include this instantaneous term in both approaches and investigate its effect on the phase diagram and dynamically screened interaction. We show that the largest deviations between previously presented EDMFT and GWGWGW+EDMFT results originate from the nonlocal Fock term, and that the quantitative differences are especially large in the strong-coupling limit. Furthermore, we show that the charge-ordering phase diagram obtained in GWGWGW+EDMFT methods for moderate interaction values is very similar to the one predicted by dual-boson methods that include the fermion-boson or four-point vertex.
We consider the thermodynamic consistency of the charge response function in the (extended) Hubbard model. In dynamical mean-field theory (DMFT), thermodynamic consistency is preserved. We prove that the static, homogeneous DMFT susceptibility is consistent as long as vertex corrections obtained from the two-particle impurity correlation function are included. In the presence of a nonlocal interaction, the problem may be treated within extended DMFT (EDMFT), or its diagrammatic extension, the dual boson approach. We show that here maintaining thermodynamic consistency requires knowledge of three- and four-particle impurity correlation functions, which are typically neglected. Nevertheless, the dual boson approximation to the response is remarkably close to consistency. This holds even when two-particle vertex corrections are neglected. EDMFT is consistent only in the strongly correlated regime and near half-filling, where the physics is predominantly local.