Many-body Coherent Potential Approximation Research Articles

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.

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...

Coherent potential approximation and projection operators for interacting electrons

A theory of the single-particle excitation spectrum is presented on the basis of the projection operator method combined with the many-body coherent-potential approximation (CPA). The theory describes the dynamics of the excitations by means of an energy-dependent Liouville operator accompanied by a coherent potential which is determined by the self-consistent CPA condition. It is shown that the present theory is essentially equivalent to the dynamical CPA and the dynamical mean-field theory. The Hubbard III approximation and the modified perturbation theory are rederived from the theory. A renormalized perturbation scheme for the Green function is developed on the basis of a general formula for the memory function. It interpolates between the weak- and strong-Coulomb interaction limits, and yields the metal-insulator transition for half-filled bands. Numerical calculations have been performed for the Gutzwiller-Hubbard model on a hypercubic lattice in infinite dimensions. The results show that the theory describes quantitatively the quasiparticle weight vs Coulomb interaction curve, yielding a reasonable critical Coulomb interaction for the metal-insulator transition. It produces the overall features of the excitation spectra and the momentum distributions for various Coulomb interaction strengths.

Spectral function of electron-phonon models by cluster perturbation theory

Cluster perturbation theory in combination with the Lanczos method is used to compute the one-electron spectral function of the Holstein polaron in one and two dimensions. It is shown that the method allows reliable calculations using relatively small clusters, and at the same time significantly reduces finite-size effects. Results are compared with exact data and the relation to existing work is discussed. We also use a strong-coupling perturbation theory---equivalent to the Hubbard I approximation---to calculate the spectral function of the quarter-filled Holstein model of spinless fermions, starting from the exact atomic-limit Green function. The results agree well with previous calculations within the many-body coherent potential approximation.

Many-body coherent potential approximation, dynamical coherent potential approximation, and dynamical mean-field theory

The coherent potential approximation (CPA) is a useful tool to describe the electron correlations as well as the effects of disorder on electrons. Among various theories of correlated electron systems, the many-body CPA, the dynamical CPA, and the dynamical mean-field theory have been investigated in great detail from the viewpoint of the CPA. It is demonstrated that these three theories are equivalent to each other, so that the theories of itinerant magnetism and those of the strongly correlated electron systems are unified within the single-site approximation. This explains why the N\'eel temperatures calculated by the dynamical mean-field theory agree well with the ones calculated by the classical and adiabatic versions of the dynamical CPA, the single-site spin-fluctuation theory, and the variational approach.

Spectral properties of the Holstein double-exchangemodel and application to manganites

Calculations of one-electron spectral functions, opticalconductivity and spin-wave energy in the Holsteindouble-exchange model are made using the many-body coherentpotential approximation. Satisfactory agreement is obtained withangle-resolved photoemission results on La1.2Sr1.8Mn2O7 and optical measurements on Nd0.7Sr0.3MnO3. A pseudogap in the one-electronspectrum at the Fermi level plays an important role in bothsystems, but a small-polaron band is only predicted to exist inthe La system. A rigorous upper bound on spin-wave energies atT = 0 is derived. The spin-wave stiffness constant D decreaseswith increasing electron-phonon coupling g in a similar way tothe Curie temperature TC, but D/(kBTC)increases for large g (low TC) as observedexperimentally.

Ferromagnetism and electron-phonon coupling in the manganites

The physics of ferromagnetic doped manganites, such as \chem{La_{1-x}Ca_xMnO_3} with $x\approx0.2$--0.4, is reviewed. The concept of double exchange is discussed within the general framework of itinerant electron magnetism. The new feature in this context is the coupling of electrons to local phonon modes. Emphasis is placed on the quantum nature of the phonons and the link with polaron physics. However it is stressed that the manganites fall in an intermediate coupling regime where standard small-polaron theory does not apply. The recently-developed many-body coherent potential approximation is able to deal with this situation and Green's recent application to the Holstein double-exchange model is described. Issues addressed include the nature of the basic electronic structure, the metal-insulator transition, a unification of colossal magnetoresistance, pressure effects and the isotope effect, pseudogaps in spectroscopy and the effect of electron-phonon coupling on spin waves.

Many-body CPA for the Holstein double-exchange model

A many-body coherent potential approximation (CPA) previously developed for the double exchange (DE) model is extended to include coupling to local quantum phonons. The Holstein-DE model studied (equal to the Holstein model for zero Hund coupling) is considered to be a simple model for the colossal magnetoresistance manganites. We concentrate on effects due to the quantisation of the phonons, such as the formation of polaron subbands. The electronic spectrum and resistivity are investigated for a range of temperature and electron-phonon coupling strengths. Good agreement with experiment is found for the Curie temperature and resistivity with intermediate electron-phonon coupling strength, but phonon quantisation is found not to have a significant effect in this coupling regime.

A many-body CPA study of quantum effects in the CMR manganites

Abstract A many-body coherent potential approximation (CPA) has been developed for simple models of the colossal magnetoresistance (CMR) manganites: the double-exchange (DE) and Holstein–DE models. In the classical limit for the local spins and phonons these models are one-electron problems and are exactly solvable within DMFT. The standard CPA, which is based on getting the atomic limit correct, is equivalent to DMFT for these one-electron problems. We are interested in the many-body case of quantum local spins and phonons in which DMFT must be solved numerically; our extended CPA offers an analytically tractable approximate solution of DMFT for this case. We use our CPA to discuss quantum effects on the electronic spectrum, Curie temperature and resistivity, comparing our results with experiment. Good semi-quantitative agreement is obtained for the temperature and field dependence of the resistivity.

CPA susceptibility of the double exchange model

We use a many-body coherent potential approximation (CPA) to study the paramagnetic state of the double exchange model with finite local spins S. Our CPA treats dynamical effects due to the quantum nature of the local spins in a local approximation, becomes exact in the atomic limit, and reduces to Kubo's one-electron CPA in the empty band limit and to dynamical mean field theory (DMFT) in the classical S→∞ limit. We solve the CPA equations of motion for all S in the strong Hund coupling limit, determining all quantities self-consistently. We show that the CPA does not give a ferromagnetic transition for any S; this is due to the local spin probability distribution function P( S z ) being inaccurately obtained. We bypass this difficulty by extrapolating P( S z ) from the exact (within DMFT) S=∞ result, and obtain a magnetic transition for all S with the expected Curie laws at band filling n=0, 1 .

Magnetic susceptibility of the double-exchange model

Previously a many-body coherent potential approximation (CPA) was used to study the double-exchange (DE) model with quantum local spins S, both for S = 1/2 and for general S in the paramagnetic state. This approximation, exact in the atomic limit, was considered to be a many-body extension of Kubo's one-electron dynamical CPA for the DE model. We now extend our CPA treatment to the case of general S and spin polarization. We show that Kubo's one-electron CPA is always recovered in the empty-band limit and that our CPA is equivalent to dynamical mean-field theory in the classical spin limit. We then solve our CPA equations self-consistently to obtain the static magnetic susceptibility in the strong-coupling limit. As in the case of the CPA for the Hubbard model, we find unphysical behaviour in at half-filling and no magnetic transition for any finite S. We identify the reason for this failure of our approximation and propose a modification which gives the correct Curie-law behaviour of at half-filling and a transition to ferromagnetism for all S.

Quantum spins in the double exchange model of manganites

In the simplest double exchange model of manganites local spins S associated with Mn ions interact with electrons in the conduction band via strong ferromagnetic Hund's rule coupling. A many-body coherent potential approximation (CPA) is developed which reproduces the exact atomic limit of the model, for all S and arbitrary filling of the band, and which reduces to an earlier one-electron CPA in the low density limit. The electronic structure and resistivity are calculated in the paramagnetic state and it is found that the resistivity arising from spin scattering is far too small to explain the large values observed in the neighbourhood of the Curie temperature. Magnetic states are most easily investigated for S= 1 2 and it appears that the many-body CPA does not give a transition to ferromagnetism in this case.