Dynamical Mean-field Theory Approximation Research Articles

Parametrizations of local vertex corrections from weak to strong coupling: Importance of the Hedin three-leg vertex

In the study of correlated systems, approximations based on the dynamical mean-field theory (DMFT) provide a practical way to take local vertex corrections into account, which capture, respectively, particle-particle screening at weak coupling and the formation of the local moment at strong coupling. We show that in both limits the local vertex corrections can be efficiently parametrized in terms of single-boson exchange, such that the two-particle physics described by DMFT and its diagrammatic extensions is recovered to good approximation and at a reduced computational cost. Our investigation highlights the importance of the frequency-dependent fermion-boson coupling (Hedin vertex) for local vertex corrections. Namely, at weak coupling the fermion-spin-boson coupling suppresses the N\'eel temperature of the DMFT approximation compared to the static mean-field, whereas for large interaction it facilitates a huge enhancement of local spin-fluctuation exchange, giving rise to the effective-exchange energy scale $4t^2/U$. We find that parametrizations of the vertex which neglect the nontrivial part of the fermion-boson coupling fail qualitatively at strong coupling.

Hubbard model on the honeycomb lattice: From static and dynamical mean-field theories to lattice quantum Monte Carlo simulations

We study the one-band Hubbard model on the honeycomb lattice using a combination of quantum Monte Carlo (QMC) simulations and static as well as dynamical mean-field theory (DMFT). This model is known to show a quantum phase transition between a Dirac semi-metal and the antiferromagnetic insulator. The aim of this article is to provide a detailed comparison between these approaches by computing static properties, notably ground-state energy, single-particle gap, double occupancy, and staggered magnetization, as well as dynamical quantities such as the single-particle spectral function. At the static mean-field level local moments cannot be generated without breaking the SU(2) spin symmetry. The DMFT approximation accounts for temporal fluctuations, thus captures both the evolution of the double occupancy and the resulting local moment formation in the paramagnetic phase. As a consequence, the DMFT approximation is found to be very accurate in the Dirac semi-metallic phase where local moment formation is present and the spin correlation length small. However, in the vicinity of the fermion quantum critical point the spin correlation length diverges and the spontaneous SU(2) symmetry breaking leads to low-lying Goldstone modes in the magnetically ordered phase. The impact of these spin fluctuations on the single-particle spectral function -- \textit{waterfall} features and narrow spin-polaron bands -- is only visible in the lattice QMC approach.

Fierz Convergence Criterion: A Controlled Approach to Strongly Interacting Systems with Small Embedded Clusters.

We present an embedded-cluster method, based on the triply irreducible local expansion formalism. It turns the Fierz ambiguity, inherent to approaches based on a bosonic decoupling of local fermionic interactions, into a convergence criterion. It is based on the approximation of the three-leg vertex by a coarse-grained vertex computed from a self-consistently determined cluster impurity model. The computed self-energies are, by construction, continuous functions of momentum. We show that, in three interaction and doping regimes of the two-dimensional Hubbard model, self-energies obtained with clusters of size four only are very close to numerically exact benchmark results. We show that the Fierz parameter, which parametrizes the freedom in the Hubbard-Stratonovich decoupling, can be used as a quality control parameter. By contrast, the GW+extended dynamical mean field theory approximation with four cluster sites is shown to yield good results only in the weak-coupling regime and for a particular decoupling. Finally, we show that the vertex has spatially nonlocal components only at low Matsubara frequencies.

Conservation in two-particle self-consistent extensions of dynamical mean-field theory

Extensions of dynamical-mean-field-theory (DMFT) make use of quantum impurity models as non-perturbative and exactly solvable reference systems which are essential to treat the strong electronic correlations. Through the introduction of retarded interactions on the impurity, these approximations can be made two-particle self-consistent. This is of interest for the Hubbard model, because it allows to suppress the antiferromagnetic phase transition in two-dimensions in accordance with the Mermin-Wagner theorem, and to include the effects of bosonic fluctuations. For a physically sound description of the latter, the approximation should be conserving. In this paper we show that the mutual requirements of two-particle self-consistency and conservation lead to fundamental problems. For an approximation that is two-particle self-consistent in the charge- and longitudinal spin channel, the double occupancy of the lattice and the impurity are no longer consistent when computed from single-particle properties. For the case of self-consistency in the charge- and longitudinal as well as transversal spin channels, these requirements are even mutually exclusive so that no conserving approximation can exist. We illustrate these findings for a two-particle self-consistent and conserving DMFT approximation.

First-principles studies of the Gilbert damping and exchange interactions for half-metallic Heuslers alloys

Heusler alloys have been intensively studied due to the wide variety of properties that they exhibit. One of these properties is of particular interest for technological applications, i.e., the fact that some Heusler alloys are half-metallic. In the following, a systematic study of the magnetic properties of three different Heusler families ${\mathrm{Co}}_{2}\mathrm{Mn}\mathrm{Z},{\text{Co}}_{2}\text{Fe}\text{Z}$, and ${\mathrm{Mn}}_{2}\mathrm{V}\mathrm{Z}$ with $\text{Z}=\left(\text{Al,}\phantom{\rule{4.pt}{0ex}}\text{Si,}\phantom{\rule{4.pt}{0ex}}\text{Ga,}\phantom{\rule{4.pt}{0ex}}\text{Ge}\right)$ is performed. A key aspect is the determination of the Gilbert damping from first-principles calculations, with special focus on the role played by different approximations, the effect that substitutional disorder and temperature effects. Heisenberg exchange interactions and critical temperature for the alloys are also calculated as well as magnon dispersion relations for representative systems, the ferromagnetic ${\mathrm{Co}}_{2}\mathrm{Fe}\mathrm{Si}$ and the ferrimagnetic ${\mathrm{Mn}}_{2}\mathrm{V}\mathrm{Al}$. Correlation effects beyond standard density-functional theory are treated using both the local spin density approximation including the Hubbard $U$ and the local spin density approximation plus dynamical mean field theory approximation, which allows one to determine if dynamical self-energy corrections can remedy some of the inconsistencies which were previously reported for these alloys.

Dynamical mean-field theory for molecules and nanostructures

Dynamical mean-field theory (DMFT) has established itself as a reliable and well-controlled approximation to study correlation effects in bulk solids and also two-dimensional systems. In combination with standard density-functional theory (DFT), it has been successfully applied to study materials in which localized electronic states play an important role. It was recently shown that this approach can also be successfully applied to study correlation effects in nanostructures. Here, we provide some details on our recently proposed DFT+DMFT approach to study the magnetic properties of nanosystems [V. Turkowski, A. Kabir, N. Nayyar, and T. S. Rahman, J. Phys.: Condens. Matter 22, 462202 (2010)] and apply it to examine the magnetic properties of small FePt clusters. We demonstrate that DMFT produces meaningful results even for such small systems. For benchmarking and better comparison with results obtained using DFT+U, we also include the case of small Fe clusters. As in the case of bulk systems, the latter approach tends to overestimate correlation effects in nanostructures. Finally, we discuss possible ways to further improve the nano-DFT+DMFT approximation and to extend its application to molecules and nanoparticles on substrates and to nonequilibrium phenomena.

Competition between Kondo and RKKY correlations in the presence of strong randomness

We propose that competition between Kondo and magnetic correlations results in a novel universality class for heavy fermion quantum criticality in the presence of strong randomness. Starting from an Anderson lattice model with disorder, we derive an effective local field theory in the dynamical mean-field theory approximation, where randomness is introduced into both hybridization and Ruderman–Kittel–Kasuya–Yosida (RKKY) interactions. Performing the saddle-point analysis in the U(1) slave-boson representation, we reveal its phase diagram which shows a quantum phase transition from a spin liquid state to a local Fermi liquid phase. In contrast with the clean limit case of the Anderson lattice model, the effective hybridization given by holon condensation turns out to vanish, resulting from the zero mean value of the hybridization coupling constant. However, we show that the holon density becomes finite when the variance of the hybridization is sufficiently larger than that of the RKKY coupling, giving rise to the Kondo effect. On the other hand, when the variance of the hybridization becomes smaller than that of the RKKY coupling, the Kondo effect disappears, resulting in a fully symmetric paramagnetic state, adiabatically connected to the spin liquid state of the disordered Heisenberg model. We investigate the quantum critical point beyond the mean-field approximation. Introducing quantum corrections fully self-consistently in the non-crossing approximation, we prove that the local charge susceptibility has exactly the same critical exponent as the local spin susceptibility, suggesting an enhanced symmetry at the local quantum critical point. This leads us to propose novel duality between the Kondo singlet phase and the critical local moment state beyond the Landau–Ginzburg–Wilson paradigm. The Landau–Ginzburg–Wilson forbidden duality serves the mechanism of electron fractionalization in critical impurity dynamics, where such fractionalized excitations are identified with topological excitations.

Phonons and the coherence scale of models of heavy fermions

We consider models of heavy fermions in the strong coupling or local moment limit and include phonon degrees of freedom on the conduction electrons. Due to the large mass or low coherence temperature of the heavy fermion state, it is shown that such a regime is dominated by vertex corrections which leads to the complete failure of the Migdal theorem. Even at weak electron-phonon couplings, binding of the conduction electrons competes with the Kondo effect and substantially reduces the coherence temperature, ultimately leading to the Kondo breakdown. Those results are obtained using a combination of the slave boson method and Migdal-Eliashberg approximation as well as the dynamical mean-field theory approximation.

Dynamical mean-field theory within an augmented plane-wave framework: Assessing electronic correlations in the iron pnictide LaFeAsO

We present an approach that combines the local-density approximation (LDA) and the dynamical mean-field theory (DMFT) in the framework of the full-potential linear augmented plane-wave method. Wannier-type functions for the correlated shell are constructed by projecting local orbitals onto a set of Bloch eigenstates located within a certain energy window. The screened Coulomb interaction and Hund's coupling are calculated from a first-principles constrained random-phase approximation scheme. We apply this $\text{LDA}+\text{DMFT}$ implementation, in conjunction with a continuous-time quantum Monte Carlo algorithm, to the study of electronic correlations in LaFeAsO. Our findings support the physical picture of a metal with intermediate correlations. The average value of the mass renormalization of the $\text{Fe}\text{ }3d$ bands is about 1.6, in reasonable agreement with the picture inferred from photoemission experiments. The discrepancies between different $\text{LDA}+\text{DMFT}$ calculations (all technically correct) which have been reported in the literature are shown to have two causes: (i) the specific value of the interaction parameters used in these calculations and (ii) the degree of localization of the Wannier orbitals chosen to represent the $\text{Fe}\text{ }3d$ states, to which many-body terms are applied. The latter is a fundamental issue in the application of many-body calculations, such as DMFT, in a realistic setting. We provide strong evidence that the DMFT approximation is more accurate and more straightforward to implement when well-localized orbitals are constructed from a large energy window encompassing $\text{Fe-}3d$, $\text{As-}4p$, and $\text{O-}2p$ and point out several difficulties associated with the use of extended Wannier functions associated with the low-energy iron bands. Some of these issues have important physical consequences regarding, in particular, the sensitivity to the Hund's coupling.

Implications of the low-temperature instability of dynamical mean-field theory for double-exchange systems

The single-site dynamical mean field theory approximation to the double exchange model is found to exhibit a previously unnoticed instability, in which a well-defined ground state which is stable against small perturbations is found to be unstable to large-amplitude but purely local fluctuations. The instability is shown to arise either from phase separation or, in a narrow parameter regime, from the presence of a competing phase. The instability is therefore suggested as a computationally inexpensive means of locating regimes of parameter space in which phase separation occurs.