On the functional integral approach in quantum statistics: I. Some approximations

Dai, Xianxi

doi:10.1088/0953-8984/3/24/009

Cited by 11 publications

(13 citation statements)

References 21 publications

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“…Especially it describes the Kondo behavior quantitatively in the strong correlation limit. 20 We showed within the single band model that the dynamical CPA+HA yields the band narrowing of quasiparticle states and the satellite peak in Fe and Ni, which were not explained by the early theories with use of the static approximation. The theory was however based on the single-band Hubbard model.…”

Section: Introductionmentioning

confidence: 76%

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

et al. 2008

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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 2nd-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 µB for Fe and 1.2 µB for Ni, explaining the experimental data. But calculated Curie temperatures are 2020 K for Fe and 1260 K for Ni, being still overestimated by a factor of two as compared with the experimental ones. Dynamical effects on electronic and magnetic properties are discussed by comparing with those in the static approximations.

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Section: Introductionmentioning

confidence: 76%

“…The approximation yields the result of the second-order perturbation in the weak Coulomb interaction limit, and describes the Kondo anomaly in the strong interaction limit. 20 Let us now calculate D ν in eq. ( 55).…”

Section: Harmonic Approximation To the Dynamical Cpamentioning

confidence: 99%

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

et al. 2008

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“…Here [ ] v means to take the derivative of a quantity fixing the static potential v (15) and (17) form a set of self-consistent equations to determine the coherent potential {Σ iσ (iω l )} and the chemical potential ǫ 0 −µ. However it is time consuming to solve the CPA equation (15) because one has to take the average eff at each frequency ω l . The following decoupling approximation simplifies the numerical calculations.…”

Section: Dynamical Cpa In the Ferro-and Antiferromagnetic Statesmentioning

confidence: 99%

Quantitative Aspects of the Dynamical Coherent Potential Approximation in Harmonic Approximation

et al. 2011

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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 magnetization, the magnetizations, susceptibilities, and the Néel temperatures (TN) as well as the Curie temperatures calculated by the Quantum Monte-Carlo (QMC) method. The critical Coulomb interactions (Uc) for the metal-insulator (MI) transition are also shown to agree with the QMC results above TN. Below TN, Uc 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 order to describe the MI transition quantitatively at low temperatures.

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“…Here (H 0 ) iLσjL ′ σ is the one-electron Hamiltonian matrix for the noninteracting Hamiltonian H 0 , and (15) has been obtained within the harmonic approximation 20,21,37,38 . It is based on an expansion of E dyn (ξ) with respect to the frequency mode of the dynamical potential v Lσσ ′ (iω ν ), where ω ν = 2νπ/β.…”

Section: First-principles Tb-lmto Dynamical Cpamentioning

confidence: 99%

Dynamical coherent-potential approximation approach to excitation spectra in3dtransition metals

2010

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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.

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On the functional integral approach in quantum statistics: I. Some approximations

Cited by 11 publications

References 21 publications

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

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

Quantitative Aspects of the Dynamical Coherent Potential Approximation in Harmonic Approximation

Dynamical coherent-potential approximation approach to excitation spectra in3dtransition metals

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