Iterative Perturbation Theory Research Articles

Electronic structure and effects of dynamical electron correlation in ferromagnetic bcc Fe, fcc Ni, and antiferromagnetic NiO

We have constructed a $\text{LDA}+\text{DMFT}$ method in the framework of the iterative perturbation theory with local density approximation (full-LDA) Hamiltonian without mapping onto the effective Wannier orbitals. We then apply this $\text{LDA}+\text{DMFT}$ method to ferromagnetic bcc Fe and fcc Ni as a test of transition metal, and to antiferromagnetic NiO as an example of transition metal oxide. In Fe and Ni, the width of occupied $3d$ bands is narrower than those in LDA and Ni 6 eV satellite appears. In NiO, the resultant electronic structure is of charge-transfer insulator type and the band gap is 4.3 eV. These results are in good agreement with the experimental x-ray photoemission spectroscopy. The configuration mixing and dynamical correlation effects play a crucial role in these results.

Dynamical Mean Field within Iterative Perturbation Theory

The problem of strong correlations belongs to the central problem of the condensed matter theory and has intensively been studied by many sophisticated methods. One of them is the dynamical mean field theory (DMFT) [1], which was successfully used to study, e.g. the metal–insulator (Mott) [2] transitions in strongly correlated electron systems. The simplest but nontrivial model that is used to study electron correlations is the Hubbard model, which in the limit of the infinite dimensions, is mapped onto a single impurity Anderson model. However, the Anderson-like models have to be solved together with appropriate self-consistent equations. In the limit of infinite dimension all spatial degrees of freedom are frozen and the self-energy is local (independent of momentum). To solve the mapped single impurity model, one can adopt several computational schemes such as the quantum Monte Carlo method, the non-crossing approximation, the exact diagonalization method or iterative perturbation theory (IPT). The last scheme (i.e. IPT), introduced for the Hubbard model at half-filling [3, 4] and in [5] for arbitrary doping, allows us to solve the single impurity Anderson model in a very efficient and relatively simple way. The objective of this paper is to discuss the numerical implementations of IPT for orbitally degenerated models.

EQUATION-OF-MOTION APPROACH TO DYNAMICAL MEAN FIELD THEORY

We propose using an equation-of-motion approach as an impurity solver for dynamical mean field theory. As an illustration of this technique, we consider a finite-U Hubbard model defined on the Bethe lattice with infinite connectivity at arbitrary filling. Depending on the filling, the spectra that is obtained exhibits a quasiparticle peak, and lower and upper Hubbard bands as typical features of strongly correlated materials. The results are also compared and in good agreement with exact diagonalization. We also find a different picture of the spectral weight transfer than the iterative perturbation theory.

Calculation of optical conductivity, resistivity and thermopower of semimetallic [formula omitted

A simplified tight-binding model, which captures the essential features of the semimetallic energy band, is proposed for the filled-skutterudite compound CeRu 4 Sb 12 . Calculation of the resistivity, Seebeck coefficient, thermopower and the optical conductivity is performed by the dynamical mean field approximation and iterative perturbation theory including the strong correlation effects. The results explain the experiments rather well.

Optical conductivity of bad metals: Shift of the Drude peak

Temperature dependence of the resistivity and the optical conductivity spectrum for the Hubbard model are investigated using the dynamical mean-field theory with the iterated perturbation theory. In the strongly correlated metallic state realized with large $U$ (the on-site repulsion energy) near the half-filling, the resistivity increases monotonously even above the Ioffe-Regel limit temperature ${T}_{\mathrm{IR}}$, which corresponds to the temperature above which a mean free path of a conduction electron is shorter than a lattice constant. As for the optical conductivity, the spectrum has the Drude peak at $\ensuremath{\omega}=0$ at low temperature, whereas the peak shifts to finite energy above ${T}_{\mathrm{IR}}$. The present results correspond to recent experimental results of optical conductivity measurements for bad metals in strongly correlated electron systems such as high-${T}_{\mathrm{c}}$ superconductors and manganites.

Calculation of Optical Conductivity, Resistivity and Thermopower of Filled Skutterudite CeRu4Sb12based on a Realistic Tight-binding Model with Strong Correlation

The filled-skutterudite compound CeRu$_4$Sb$_{12}$ shows a pseudo-gap structure in the optical conductivity spectra similar to the Kondo insulators, but metallic behavior below 80 K. The resistivity shows a large peak at 80 K, and the Seebeck coefficient is positive and also shows a large peak at nearly the same temperature. In order to explain all these features, a simplified tight-binding model, which captures the essential features of the band calculation, is proposed. Using this model and introducing the correlation effect within the framework of the dynamical mean field approximation and the iterative perturbation theory, the temperature dependences of the optical conductivity, resistivity and the Seebeck coefficient are calculated, which can explain the experiments.

Influence of Spatial Correlations in Strongly Correlated Electron Systems: Extension to Dynamical Mean Field Approximation

We propose a formalism to take account of the correction of the spatial fluctuations to the local self-energy obtained by the dynamical mean-field approximation. For this purpose, the approximate dynamical susceptibility in the framework of the iterated perturbation theory is proposed and examined. Using the formalism, it is demonstrated that the one-particle spectral intensity in the two-dimensional Hubbard model at half-filling exhibits the pseudo-gap behavior in the central coherent quasiparticle peak due to the critical antiferromagnetic fluctuation. The specific heat is considerably enhanced by the short-range order, which assists a tendency of the Mott localization showing the reduction of the double occupancy. We briefly discuss a formulation for the superconducting transition temperature in the present approximation.

Orbital-selective Mott transitions in the anisotropic two-band Hubbard model at finite temperatures

The anisotropic degenerate two-orbital Hubbard model is studied within dynamical mean-field theory at low temperatures. High-precision calculations on the basis of a refined quantum Monte Carlo (QMC) method reveal that two distinct orbital-selective Mott transitions occur for a bandwidth ratio of 2, even in the absence of spin-flip contributions to the Hund exchange. The second transition---not seen in earlier studies using QMC, iterative perturbation theory, and exact diagonalization---is clearly exposed in a low-frequency analysis of the self-energy and in local spectra.

BCS-BEC crossover atT=0: A dynamical mean-field theory approach

We study the $T=0$ crossover from the BCS superconductivity to Bose-Einstein condensation in the attractive Hubbard Model within dynamical mean field theory (DMFT) in order to examine the validity of Hartree-Fock-Bogoliubov (HFB) mean field theory, usually used to describe this crossover, and to explore the physics beyond it. Quantum fluctuations are incorporated using iterated perturbation theory as the DMFT impurity solver. We find that these fluctuations lead to large quantitative effects in the intermediate coupling regime, leading to a reduction of both the superconducting order parameter and the energy gap relative to the HFB results. A qualitative change is found in the single-electron spectral function, which now shows an incoherent spectral weight for energies larger than three times the gap, in addition to the usual Bogoliubov quasiparticle peaks.

K-Dependent Spectrum and Optical Conductivity near Metal–Insulator Transition in Multi-Orbital Hubbard Bands

We apply the dynamical mean field theory (DMFT) combined with the iterative perturbation theory (IPT) to the doubly degenerate e g and the triply degenerate t 2g bands on a simple cubic lattice and a body-centered cubic lattice and calculate the spectrum and optical conductivity in arbitrary electron occupation. The spectrum simultaneously shows the effects of multiplet structure together with the electron ionization and affinity levels of different electron occupations, coherent peaks at the Fermi energy in the metallic phase and an energy gap at an integer filling of electrons for sufficiently large Coulomb U . We also discuss the critical value of the Coulomb U for degenerate orbitals on a simple cubic lattice and a body-centered cubic lattice.

Single Mott transition in the multiorbital Hubbard model

The Mott transition in a multi-orbital Hubbard model involving subbands of different widths is studied within the dynamical mean field theory. Using the iterated perturbation theory for the quantum impurity problem it is shown that at low temperatures inter-orbital Coulomb interactions give rise to a single first-order transition rather than a sequence of orbital selective transitions. Impurity calculations based on the Quantum Monte Carlo method confirm this qualitative behavior. Nevertheless, at finite temperatures, the degree of metallic or insulating behavior of the subbands differs greatly. Thus, on the metallic side of the transition, the narrow band can exhibit quasi-insulating features, whereas on the insulating side the wide band exhibits pronounced bad-metal behavior. This complexity might partly explain contradictory results between several previous works.

Fourth-order perturbation theory for the half-filled Hubbard model in infinite dimensions

We calculate the zero-temperature self-energy to fourth-order perturbation theory in the Hubbard interaction $U$ for the half-filled Hubbard model in infinite dimensions. For the Bethe lattice with bare bandwidth $W$, we compare our perturbative results for the self-energy, the single-particle density of states, and the momentum distribution to those from approximate analytical and numerical studies of the model. Results for the density of states from perturbation theory at $U/W=0.4$ agree very well with those from the Dynamical Mean-Field Theory treated with the Fixed-Energy Exact Diagonalization and with the Dynamical Density-Matrix Renormalization Group. In contrast, our results reveal the limited resolution of the Numerical Renormalization Group approach in treating the Hubbard bands. The momentum distributions from all approximate studies of the model are very similar in the regime where perturbation theory is applicable, $U/W \le 0.6$. Iterated Perturbation Theory overestimates the quasiparticle weight above such moderate interaction strengths.

Disordered local moments formation in high-dimensional strongly correlated materials

We have investigated the electronic properties of strongly correlated materials including the possibility of disordered local moments formation in the framework of the dynamical mean-field theory. We use a self-consistent generalization of the iterated perturbation theory and calculate the value of local moment amplitudes. Low-energy behavior and temperature dependence of local moments is also examined.

Generalization of the Iterative Perturbation Theory and Metal–Insulator Transition in Multi-Orbital Hubbard Bands

The iterative perturbation theory of the dynamical mean field theory is generalized to arbitrary electron occupation for multi-orbital Hubbard bands. We present numerical results for doubly degener...

Is There Really No Extensive Self-Consistent Perturbation Theory?

Many-particle perturbation theory is dominated by the Rayleigh–Schrodinger expansion, because at fixed particle density each term of the power series in the strength of the interaction has the right dependence on the particle number N. The first self-consistent generalization, the Brillouin–Wigner expansion, however, is non-extensive already in 2nd order. In Feenberg's generalization the same feature is found within iterative perturbation theory, but the series can be rearranged in such a way that lower orders are extensive. Applications are suggested.

Effect of strong correlations and static diagonal disorder in thed=∞Hubbard model

We investigate the effects of static, diagonal disorder in the $d=\ensuremath{\infty}$ Hubbard model by treating the dynamical effects of local Hubbard correlations and disorder on an equal footing. This is achieved by a proper combination of the iterated perturbation theory and the coherent-potential approximation. Within the paramagnetic phase, we find that the renormalized Fermi-liquid metal phase of the pure Hubbard model is stable against disorder for small disorder strengths. With increasing disorder, strong resonant scattering effects destroy low-energy Fermi-liquid coherence, leading to an incoherent metallic state off half-filling. Finally, for large enough disorder, a continuous transition to the disordered insulating phase occurs. The nature of the incoherent metallic phase, as well as the effects of the low-energy coherence (incoherence) on optical conductivity and electronic Raman spectra, are considered in detail.

REALISTIC MODELING OF STRONGLY CORRELATED ELECTRON SYSTEMS: AN INTRODUCTION TO THE LDA+DMFT APPROACH

The LDA+DMFT approach merges conventional band structure theory in the local density approximation (LDA) with a state-of-the-art many-body technique, the dynamical mean-field theory (DMFT). This new computational scheme has recently become a powerful tool for ab initio investigations of real materials with strong electronic correlations. In this paper an introduction to the basic ideas and the set-up of the LDA+DMFT approach is given. Results for the photoemission spectra of the transition metal oxide La 1-x Sr x TiO 3, obtained by solving the DMFT equations by quantum Monte Carlo (QMC) simulations, are presented and are found to be in very good agreement with experiment. The numerically exact DMFT(QMC) solution is compared with results obtained by two approximative solutions, i.e. the iterative perturbation theory and the non-crossing approximation.

Toward a systematic1/dexpansion: Two-particle properties

We present a procedure to calculate 1/d corrections to the two-particle properties around the infinite dimensional dynamical mean field limit. Our method is based on a modified version of the scheme of Ref. onlinecite{SchillerIngersent}}. To test our method we study the Hubbard model at half filling within the fluctuation exchange approximation (FLEX), a selfconsistent generalization of iterative perturbation theory. Apart from the inherent unstabilities of FLEX, our method is stable and results in causal solutions. We find that 1/d corrections to the local approximation are relatively small in the Hubbard model.

Correlation Effects on the Double Exchange Model in a Ferromagnetic Metallic Phase

The effect of the Hubbard interaction among conduction electrons on the double exchange model is investigated in a ferromagnetic metallic phase. Applying iterative perturbation theory to the Hubbard interaction within dynamical mean field theory, we calculate the one-particle spectral function and the optical conductivity, in which coherent-potential approximation is further used to treat the ferromagnetic Hund coupling between conduction electrons and localized spins. Identifying the decrease of the magnetization for the localized spin with the increase of the temperature, we discuss the temperature dependence of the one-particle spectrum and the optical conductivity. It is found that the interplay between the Hund coupling and the Hubbard interaction dramatically changes the spectral function, while it is somehow obscured in the optical conductivity.

Unified theory of dynamical mean field and self-consistently renormalized spin-fluctuations

A unified theory of the dynamical mean-field and the self-consistently renormalized spin-fluctuations (SCR) for strongly correlated electron systems is proposed. Starting from the iterative perturbation theory, local dynamical magnetic susceptibility χ L( ω) is constructed with inclusion of the vertex corrections, and the effect of spin fluctuations is incorporated in the form similar to the SCR theory. Temperature dependence of specific heat and electrical resistivity are calculated to be proportional to T(1− const. T ) and T 3/2, respectively, at the quantum critical point and low temperatures.