Dynamical Coherent Potential Approximation Research Articles

Out of time order correlation of the Hubbard model with random local disorder.

The out-of-time-order correlator (OTOC) serves as a powerful tool for investigating quantum information spreading and chaos in complex systems. We present a method employing non-equilibrium dynamical mean-field theory and coherent potential approximation combined with diagrammatic perturbation on the Schwinger-Keldysh contour to calculate the OTOC for correlated fermionic systems subjected to both random disorder and electron interaction. Our key finding is that random disorder enhances the OTOC decay in the Hubbard model for the metallic phase in the weakly interacting limit. However, the current limitation of our perturbative solver restricts the applicability to weak interaction regimes.

First-Principles Momentum Dependent Local Ansatz Approach to the Ground-State Properties of Iron-Group Transition Metals

The ground-state properties of iron-group transition metals from Sc to Cu have been investigated on the basis of the first-principles momentum dependent local ansatz (MLA) theory. Correlation energy gain is found to show large values for Mn and Fe: 0.090 Ry (Mn) and 0.094 Ry (Fe). The Hund-rule coupling energies are found to be 3000 K (Fe), 1400 K (Co), and 300 K (Ni). It is sugested that these values can resolve the inconsistency in magnetic energy between the density functional theory and the first-principles dynamical coherent potential approximation theory at finite temperatures. Charge fluctuations are shown to be suppressed by the intra-orbital correlations and inter-orbital charge-charge correlations, so that they show nearly constant values from V to Fe: 1.57 (V and Cr), 1.52 (Mn), and 1.44 (Fe), which are roughly twice as large as those obtained by the $d$ band model. The amplitudes of local moments are enhanced by the intra-orbital and inter-orbital spin-spin correlations and show large values for Mn and Fe: 2.87 (Mn) and 2.58 (Fe). These values are in good agreement with the experimental values estimated from the effective Bohr magneton number and the inner core photoemission data.

Conduction electron states and ferromagnetism of electron-doped EuO

To study the conduction electron states and ferromagnetism of electron-doped EuO theoretically, we have applied two approximations to the s-f model and compared their results: virtual crystal approximation (VCA) and dynamical coherent potential approximation (dynamical CPA). The results of both approximations explain the anomalous magnetization curve experimentally observed in Gd-doped EuO and/or Eu-rich EuO with a low electron density, while only the result of dynamical CPA can explain the electron-density dependence of the Curie temperature TC. The TC calculated by VCA shows the monotonous increase with electron density, while the TC calculated by dynamical CPA shows a maximum for a certain electron density. The mechanism of TC increase is also discussed.

Electronic and magnetic properties of Gd-doped EuO

To study electron states and magnetism in Gd-doped EuO theoretically, we first calculate the spin-polarized density of states (DOS) by applying the dynamical coherent potential approximation (dynamical CPA) for two simple models: the $s$-$f$ model of electron-doped EuO and a model of Eu${}_{1\ensuremath{-}x}$Gd${}_{x}$O. On the basis of the spin-polarized DOS, we calculate the total energy of electrons interacting with $f$ spins through an exchange interaction. Then, we obtain the magnetization as a function of the temperature $T$, by minimizing the free energy. We discuss the mechanism of the electron-induced increase in the Curie temperature ${T}_{C}$, the origin of the anomalous magnetization curve, and the existence of a threshold Gd concentration for increasing ${T}_{C}$. We investigate the effect of on-site attractive potential that yields an impurity level when the Gd concentration is low. We also discuss the relationship between the redshift of the optical absorption edge and the increase in the ${T}_{C}$ of Gd-doped EuO.

Single-polaron properties in the one-dimensional Holstein and SSH models

We study the single-polaron properties of the one-dimensional Holstein and SSH model. The dynamical coherent potential approximation (under the Hartree approximation) is applied to compute the polaron dispersion, the quasi-particle residue, and the polaronʼs Greenʼs functions. We compare our calculated results in comparison with those by the self-consistent Born approximation plus higher-order diagrams.

Quantitative Aspects of the Dynamical Coherent Potential Approximation in Harmonic Approximation

Magnetic and electronic properties of the Hubbard model on the Bethe and fcc lattices in infinite dimensions have been investigated numerically on the basis of the dynamical coherent potential approximation (CPA) theory combined with the harmonic approximation (HA) in order to clarify the quantitative aspects of the theory. It is shown that the dynamical CPA+HA reproduces well the sublattice magnetizations, the magnetizations, susceptibilities, and the Neel temperatures ( T N ) as well as the Curie temperatures calculated by the Quantum Monte-Carlo (QMC) method. The critical Coulomb interactions ( U c ) for the metal–insulator (MI) transition are also shown to agree with the QMC results above T N . Below T N , U c deviate from the QMC values by about 30% at low temperature regime. These results indicate that the dynamical CPA+HA is applicable to the quantitative description of the magnetic properties in high dimensional systems, but one needs to take into account higher-order dynamical corrections in orde...

Ferromagnetism of transition metals and screened exchange interactions

We have investigated the magnetic properties of Fe, Co, and Ni at finite temperatures on the basis of the first-principles dynamical coherent potential approximation (CPA) in order to clarify the role of the exchange interaction energy ($J$) screened by {\it sp} electrons and its applicability to finite-temperature magnetism. With use of the atomic $J$, we obtained the Curie temperatures ($T_{\rm C}$) 1930 K for Fe and 2550 K for fcc Co, which are overestimated by a factor of 1.8 as compared with the experimental values, while we obtained $T_{\rm C}=620$ K for Ni being in good agreement with the experiment. Calculated effective Bohr magneton numbers also quantitatively agree with the experimental values. By comparing the results with those obtained by the screened $J$ and by comparing them with the experiments, we found that the screened $J$, which are reduced by 30% as compared with the atomic ones, improve the ground-state magnetizations and densities of states at low temperatures in Fe and fcc Co, as well as $T_{\rm C}$ in fcc Co. But the screened $J$ yield worse results for finite temperature properties of Fe and underestimate both the ground-state magnetization and $T_{\rm C}$ in case of Ni. We discuss possible origins for these inconsistencies.

First-Principles Dynamical Coherent-Potential Approximation Approach to the Ferromagnetism of Fe, Co, and Ni

Magnetic properties of Fe, Co, and Ni at finite temperatures have been investigated on the basis of the first-principles dynamical CPA (Coherent Potential Approximation) combined with the LDA (Local Density Approximation) + $U$ Hamiltonian in the Tight-Binding Linear Muffintin Orbital (TB-LMTO) representation. The Hamiltonian includes the transverse spin fluctuation terms. Numerical calculations have been performed within the harmonic approximation with 4th-order dynamical corrections. Calculated single-particle densities of states in the ferromagnetic state indicate that the dynamical effects reduce the exchange splitting, suppress the band width of the quasi-particle state, and causes incoherent excitations corresponding the 6 eV satellites. Results of the magnetization vs temperature curves, paramagnetic spin susceptibilities, and the amplitudes of local moments are presented. Calculated Curie temperatures ($T_{\rm C}$) are reported to be 1930K for Fe, 2550K for Co, and 620K for Ni; $T_{\rm C}$ for Fe and Co are overestimated by a factor of 1.8, while $T_{\rm C}$ in Ni agrees with the experimental result. Effective Bohr magneton numbers calculated from the inverse susceptibilities are 3.0 $\mu_{\rm B}$ (Fe), 3.0 $\mu_{\rm B}$ (Co), and 1.6 $\mu_{\rm B}$ (Ni), being in agreement with the experimental ones. Overestimate of $T_{\rm C}$ in Fe and Co is attributed to the neglects of the higher-order dynamical effects as well as the magnetic short range order.

Dynamical coherent-potential approximation approach to excitation spectra in3dtransition metals

First-principles dynamical CPA (Coherent-Potential Approximation) for electron correlations has been developed further by taking into account higher-order dynamical corrections with use of the asymptotic approximation. The theory is applied to the investigations of a systematic change of excitation spectra in $3d$ transition metals from Sc to Cu at finite temperatures. It is shown that the dynamical effects damp main peaks in the densities of states (DOS) obtained by the local density approximation to the density functional theory, reduce the band broadening due to thermal spin fluctuations, create the Mott-Hubbard type bands in the case of fcc Mn and fcc Fe, and create a small hump corresponding to the `6 eV' satellite in the case of Co, Ni, and Cu. Calculated DOS explain the X-ray photoelectron spectroscopy data as well as the bremsstrahlung isochromat spectroscopy data. Moreover, it is found that screening effects on the exchange energy parameters are significant for understanding the spectra in magnetic transition metals.

Carrier States in Ferromagnetic Semiconductors and Diluted Magnetic Semiconductors—Coherent Potential Approach—

The theoretical study of magnetic semiconductors using the dynamical coherent potential approximation (dynamical CPA) is briefly reviewed. First, we give the results for ferromagnetic semiconductors (FMSs) such as EuO and EuS by applying the dynamical CPA to the s-f model. Next, applying the dynamical CPA to a simple model for AMnB-type diluted magnetic semiconductors (DMSs), we show the results for three typical cases to clarify the nature and properties of the carrier states in DMSs. On the basis of this model, we discuss the difference in the optical band edges between II-V DMSs and III-V-based DMSs, and show that two types of ferromagnetism can occur in DMSs when carriers are introduced. The carrier-induced ferromagnetism of GaMnAs is ascribed to a double-exchange (DE)-like mechanism realized in the magnetic impurity band/or in the band tail.

First-principles dynamical CPA to finite-temperature magnetism of transition metals

We present here the first-principles dynamical CPA (coherent potential approximation) combined with the tight-binding LMTO LDA+U method towards quantitative calculations of the electronic structure and magnetism at finite temperatures in transition metals and compounds. The theory takes into account the single-site dynamical charge and spin fluctuations using the functional integral technique as well as an effective medium. Numerical results for Fe, Co, and Ni show that the theory explains quantitatively the high-temperature properties such as the effective Bohr magneton numbers and the excitation spectra in the paramagnetic state, and describes the Curie temperatures semiquantitatively.

Evidence of Strong Electron Correlations in γ-Iron

Single-particle excitation spectra of gamma-Fe in the paramagnetic state have been investigated by means of the first-principles dynamical coherent potential approximation theory which has recently been developed. It is found that the central peak in the density of states consisting of the t2g bands is destroyed by electron correlations, and the Mott-Hubbard type correlated bands appear. The results indicate that the gamma-Fe can behave as correlated electrons at high temperatures.

Global-local ansatz and dynamical coherent potential approximation study of off-diagonal exciton-phonon coupling

We study the generalized Holstein Hamiltonian in the simultaneous presence of diagonal and off-diagonal exciton-phonon couplings using the global-local Ansatz and the dynamical coherent potential approximation (under the Hartree approximation). The former yields detailed exciton-phonon correlations for polaron states in the lowest polaron energy band in addition to the state-of-the-art ground-state wave functions, while the latter reveals polaron dynamic information in the form of extended energy spectra and spectral density functions. Lowest polaron energy bands generated by the two methods are compared.

Dynamical Coherent-Potential Approximation and Tight-Binding Linear Muffintin Orbital Approach to Correlated Electron System

Dynamical coherent-potential approximation (CPA) to correlated electrons has been extended to a system with realistic Hamiltonian which consists of the first-principles tight-binding linear muffintin orbital (LMTO) bands and intraatomic Coulomb interactions. Thermodynamic potential and self-consistent equations for Green function are obtained on the basis of the functional integral method and the harmonic approximation which neglects the mode–mode couplings between the dynamical potentials with different frequency. Numerical calculations have been performed for Fe and Ni within the second-order dynamical corrections to the static approximation. The band narrowing of the quasiparticle states and the 6 eV satellite are obtained for Ni at finite temperatures. The theory leads to the Curie–Weiss law for both Fe and Ni. Calculated effective Bohr magneton numbers are 3.0 µ B for Fe and 1.2 µ B for Ni, explaining the experimental data. But calculated Curie temperatures are 2020 K for Fe and 1260 K for Ni, being ...

Magnetism and electron correlations

Electron correlation effects on magnetism are discussed from a local point of view on the basis of the dynamical coherent potential approximation (CPA) which completely takes account of the dynamical spin and charge fluctuations within the single-site approximation. The dynamical CPA is equivalent to other single-site theories of strongly correlated electrons: the many-body CPA, the dynamical mean-field theory, and the projection operator method CPA. The method is shown to describe both the dynamical effects on magnetic properties and the many-body band structure on the same footing. The effects of orbital degeneracy and the realistic calculation scheme are discussed with emphasis on Hund's rule coupling. Two types of theories for non-local correlations, the molecular dynamics approach and the self-consistent projection operator approach, are presented. The effects of magnetic short-range order and non-local correlations are discussed with some numerical results.

Mean-field approximations for the electronic states in disordered alloys

Mean-field approximations are used to find approximate solutions to the one-electron equations for the electronic states in disordered alloys because ordinary band-theory approaches are not applicable. The first mean-field approximation, the coherent potential approximation, does not treat Coulomb effects correctly. This has been improved by changing the way the mean-field approximation is implemented. It may be that this experience with mean-field approximations will be useful to the combination of many-body theory and mean-field theory that has produced the dynamical coherent potential approximation and dynamical mean field theory for treating strongly correlated electron systems.

Single-particle spectrum for a model of fermions interacting with two-level local excitations on a lattice: A dynamical CPA approach

The problem of motion of a single electron interacting with a periodic lattice of two-level systems is investigated within a spinless fermion model. The Green's function is calculated in a single-site dynamical coherent potential approximation which is equivalent to DMFT. The picture of one-electron density of states is obtained for various values of the tunnel splitting and coupling between the electron and two-level system. The occurrence of a band splitting with increase of the coupling is demonstrated.

Optical band edge of diluted magnetic semiconductors

Applying the dynamical coherent potential approximation to a simple model, we have theoretically studied the behavior of the optical band edge in diluted magnetic semiconductors (DMS). For ${A}_{1\ensuremath{-}x}^{II}{\mathrm{Mn}}_{x}{B}^{VI}$-type DMS, the present study reveals that the linear relationship between spin splitting due to the exchange interaction $\ensuremath{\Delta}{E}_{\mathit{ex}}$ and averaged magnetization $\ensuremath{\mid}x⟨Sz⟩\ensuremath{\mid}$ widely holds for different values of $x$. The ratio, $\ensuremath{\Delta}{E}_{\mathit{ex}}∕x⟨{S}_{z}⟩$, however, does not agree with the exchange integral, but depends on both the exchange strength and the band offset. Furthermore, the present study reveals that in the low dilution of ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{As}$, the optical band edge exists not at the band edge of the impurity band but near the bottom of the host band. The optical band edge behaves as if the exchange interaction is ferromagnetic although the antiferromagnetic exchange interaction actually operates at the Mn site. We conclude that the spin-dependent shift of the carrier states between the impurity band and the host band accompanied by the change of magnetization causes the anomalous behavior of the optical band edge (the reversal of the apparent sign of the exchange integral) that was reported in the magnetoreflection measurement of ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{As}$.

Electron correlations and many-body techniques in magnetism

Recent progress in the theory of magnetism and electron correlations is reviewed to clarify the theories developed in the last decade and their mutual relations. A historical development of the theory of magnetism is outlined, and the dynamical coherent potential approximation (CPA) which completely takes account of the dynamical spin and charge fluctuations within the single-site approximation is introduced. Both the dynamical effects on various magnetic properties and the many-body band structure are shown to be explained on the same footing. It is shown that the dynamical CPA is equivalent to the other single-site theories of strongly correlated electrons: the many-body CPA, the dynamical mean-field theory (DMFT), and the projection operator method CPA (PM-CPA). These theories are elucidated with use of a common concept of effective medium or coherent potential. The effects of orbital degeneracy and the realistic calculation scheme are discussed with an emphasis on Hund’s rule coupling. Non-local theor...

Mechanism of carrier-induced ferromagnetism in diluted magnetic semiconductors

Applying the dynamical coherent potential approximation to a simple model, we have systematically studied the carrier states in $A_{1-x}$Mn$_xB$-type diluted magnetic semiconductors (DMS's). The model calculation was performed for three typical cases of DMS's: The cases with strong and moderate exchange interactions in the absence of nonmagnetic potentials, and the case with strong attractive nonmagnetic potentials in addition to moderate exchange interaction. When the exchange interaction is sufficiently strong, magnetic impurity bands split from the host band. Carriers in the magnetic impurity band mainly stay at magnetic sites, and coupling between the carrier spin and the localized spin is very strong. The hopping of the carriers among the magnetic sites causes ferromagnetism through a {\it double-exchange (DE)-like} mechanism. We have investigated the condition for the DE-like mechanism to operate in DMS's. The result reveals that the nonmagnetic attractive potential at the magnetic site assists the formation of the magnetic impurity band and makes the DE-like mechanism operative by substantially enhancing the effect of the exchange interaction. Using conventional parameters we have studied the carrier states in Ga$_{1-x}$Mn$_x$As. The result shows that the ferromagnetism is caused through the DE-like mechanism by the carriers in the bandtail originating from the impurity states.