Impact of partially bosonized collective fluctuations on electronic degrees of freedom

Abstract

In this work we present a comprehensive analysis of collective electronic fluctuations and their effect on single-particle properties of the Hubbard model. Our approach is based on a standard dual fermion/boson scheme with the interaction truncated at the two-particle level. Within this framework we compare various approximations that differ in the set of diagrams (ladder vs exact diagrammatic Monte Carlo), and/or in the form of the four-point interaction vertex (exact vs partially bosonized). This allows to evaluate the effect of all components of the four-point vertex function on the electronic self-energy. In particular, we observe that contributions that are not accounted for by the partially bosonized approximation for the vertex have only a minor effect on electronic degrees of freedom in a broad range of model parameters. In addition, we find that in the regime, where the ladder dual fermion approximation provides an accurate solution of the problem, the leading contribution to the self-energy is given by the longitudional bosonic modes. This can be explained by the fact that contributions of transverse particle-hole and particle-particle modes partially cancel each other. Our findings justify applicability of the recently introduced dual triply irreducible local expansion (D-TRILEX) method that provides one of the simplest consistent diagrammatic extensions of the dynamical mean-field theory.

Coexisting charge density wave and ferromagnetic instabilities in monolayer InSe

“…This form of the D-TRILEX susceptibility resembles the DMFT susceptibility [52][53][54] with a longitudinal dynamical vertex corrections [34]. In this case, divergences of charge and spin susceptibilities do not affect each other through the self-energy, which allows one to detect instabilities inside broken-symmetry phases.…”

“…At the same time, spatial collective electronic fluctuations and the long-range Coulomb interaction cannot be taken into account in the framework of DMFT and require to use diagrammatic extensions of this theory [32]. In this work, we solve the considered many-body problem using the dual triply irreducible local expansion (D-TRILEX) method [33][34][35]. The D-TRILEX approach is one of the simplest consistent diagrammatic extensions of DMFT that allows one to account for leading collective electronic fluctuations on equal footing without any limitation on the range.…”

“…The spatial fluctuations are considered in a partially-bosonized form of the renormalized charge (ς = c) and spin (ς = s) interactions W ς qω that enter the diagrammatic part of the self-energy Σ kν introduced beyond DMFT. Thus, the D-TRILEX method can be seen as the GW extension of the DMFT that, however, additionally considers exact local three-point vertex corrections in diagrams for the self-energy and the polarization operator [33,34]. Such vertices are of a crucial importance for a correct description of magnetic, optical and transport proper- ties of the system [35,[39][40][41][42][43][44][45][46][47][48][49].…”

“…ς qω is the total polarization operator of the problem, where Π ς qω is the diagrammatic contribution introduced in the D-TRILEX approach [33,34]. Charge and spin susceptibilities X ς qω can then be obtained straightforwardly as [35].…”

“…Therefore, the development of the CDW ordering should also be reflected in single-particle observables such as the electronic DOS. In order to account for the feedback effects of long-range collective electronic fluctuations to single-particle quantities we perform self-consistent D-TRILEX calculations [33,34] and obtain the full lattice Green's function G kν of the considered many-body problem that takes into account both, local and non-local correlation effects. Further, we take the local part of the lattice Green's function G loc ν = 1 N k G kν and perform an analytical continuation from Matsubara frequency space ν to real energies using the stochastic optimization method [55] to get the DOS.…”