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arXiv:2110.02806 · Physical review. B./Physical review. B

Generalized dynamical mean-field theory of two-sublattice systems with long-range interactions and its application to study charge and spin correlations in graphene

A. A. Katanin

Published Dec 29, 2021• 7 citations
arXivHTMLPDF

Abstract

We investigate magnetic and charge correlations in graphene by using the formulation of extended dynamical mean-field theory (E-DMFT) for two-sublattice systems. First, we map the average nonlocal interaction onto the effective static interaction between different sublattices, which is treated together with the local interaction within an effective two-orbital local model. The remaining part of the nonlocal interaction is considered by introducing an effective retarded interaction within the E-DMFT approach. The nonlocal susceptibilities in the charge and spin channel are further evaluated in the ladder approximation. We verify the applicability of the proposed method to describe the effect of uniformly screened long-range Coulomb potential $\ensuremath{\propto}1/r$, as well as screened realistic long-range electron interactions [T. O. Wehling et al., Phys. Rev. Lett. 106, 236805 (2011)] in graphene. We show that the developed approach describes a competition of semimetal, spin density wave (SDW), and charge-density-wave (CDW) correlations. The obtained phase diagram is in a good agreement with recent results of the functional renormalization group (fRG) for finite large graphene nanoflakes and scaling analysis of quantum Monte Carlo data on finite clusters. Similarly to the previously obtained results within the fRG approach, the realistic screening of Coulomb interaction by $\ensuremath{\sigma}$ bands causes moderate (strong) enhancement of critical long-range interaction strength, needed for the SDW (CDW) instability, compared to the results for the uniformly screened Coulomb potential.

DOI
10.1103/physrevb.104.245142

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We propose an approach describing correlated electronic systems within the two-particle irreducible functional renormalization-group (2PI-fRG) approach, which uses initial self-energy and the two-particle irreducible vertices, obtained from (extended) dynamical mean-field theory [E(DMFT)]. Using the 2PI-fRG approach allows us to treat both local and nonlocal interactions. In the case of purely local interaction the corresponding equations have similar (although not identical) structure to the earlier developed DMFT+fRG (DMF2RG)({\mathrm{DMF}}^{2}\mathrm{RG})(DMF2RG) approach. In a simplest truncation, neglecting scale dependence of the two-particle irreducible vertices, we reproduce the results for the two-particle vertices/susceptibilities in the ladder approximation of the dual-boson (DB) or the dynamic vertex approximation approach; in more sophisticated truncations the method allows us to consider nonlocal corrections to the self-energy as well as the interplay of charge and spin correlations. The proposed scheme is tested on the two-dimensional standard and extended $U\text{\ensuremath{-}}V$ half-filled Hubbard models. For the standard Hubbard model we obtain nonlocal self-energy, which is in agreement with numerical studies; for the extended Hubbard model we find the boundary of charge instability, which agrees well with the results of the DB approach. We also ascertain that the effect of spin correlations on electron interaction in the charge channel, not considered previously in the DB approach, only slightly reduces critical next-nearest-neighbor interaction of charge instability of the extended Hubbard model at the considered finite low temperature, yielding better agreement with dynamic cluster approximation. The considered method is rather general and can be applied to study various phenomena in strongly correlated electronic systems.
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We use the truncated-unity functional renormalization group (TUFRG) to study many-body instabilities of correlated electrons in graphene doped near the van Hove singularity (VHS). The system is described by an extended Hubbard model including several Coulomb repulsions between neighboring sites. With the repulsion parameters, which turn out to be suitable for low-energy consideration of graphene, we find a spin-bond-order phase in the vicinity of the VHS. This phase gives way to a spin-density-wave phase when involving a weak additional screening. The ground-state phase diagram is presented in the space of the doping level and the screening parameter. We describe in detail both of these spin-ordered states by using recently developed TUFRG + mean-field (MF) scheme, i.e. a combined approach of TUFRG and MF theory. The collinear states are energetically preferable in both cases of the spin bond order and the spin-density wave. But if the third-nearest-neighbor hopping is absent, these spin orders become chiral. The band structures of two collinear spin-ordered states are presented, revealing the metallic behavior of the system.
Nanostructures with open shell transition metal or molecular constituents host often strong electronic correlations and are highly sensitive to atomistic material details. This tutorial review discusses method developments and applications of theoretical approaches for the realistic description of the electronic and magnetic properties of nanostructures with correlated electrons. First, the implementation of a flexible interface between density functional theory and a variant of dynamical mean field theory (DMFT) highly suitable for the simulation of complex correlated structures is explained and illustrated. On the DMFT side, this interface is largely based on recent developments of quantum Monte Carlo and exact diagonalization techniques allowing for efficient descriptions of general four fermion Coulomb interactions, reduced symmetries and spin-orbit coupling, which are explained here. With the examples of the Cr (001) surfaces, magnetic adatoms, and molecular systems it is shown how the interplay of Hubbard U and Hund’s J determines charge and spin fluctuations and how these interactions drive different sorts of correlation effects in nanosystems. Non-local interactions and correlations present a particular challenge for the theory of low dimensional systems. We present our method developments addressing these two challenges, i.e., advancements of the dynamical vertex approximation and a combination of the constrained random phase approximation with continuum medium theories. We demonstrate how non-local interaction and correlation phenomena are controlled not only by dimensionality but also by coupling to the environment which is typically important for determining the physics of nanosystems.
We investigate the quantum many-body instabilities for electrons on the honeycomb lattice at half filling with extended interactions, motivated by a description of graphene and related materials. We employ a recently developed fermionic functional renormalization group scheme, which allows for highly resolved calculations of wave-vector dependences in the low-energy effective interactions. We encounter the expected anti-ferromagnetic spin density wave for a dominant on-site repulsion between electrons, and charge order with different modulations for dominant pure nth{n}^{\text{th}}nth nearest-neighbor repulsive interactions. Novel instabilities towards incommensurate charge density waves take place when nonlocal density interactions among several bond distances are included simultaneously. Moreover, for more realistic Coulomb potentials in graphene including enough nonlocal terms there is a suppression of charge order due to competition effects between the different charge ordering tendencies, and if the on-site term fails to dominate, the semimetallic state is rendered stable. The possibility of a topological Mott insulator being the favored tendency for dominating second-nearest-neighbor interactions is not realized in our results with high momentum resolution.