Tadashi Arai

Green's function solution of the Kondo problem and universality of the thermodynamic properties (invited)

Using a functional derivative approach, we derive, for the nondegenerate Anderson model of dilute magnetic alloys, a Green’s function, which is valid at all temperatures and which accurately exhibits the Kondo effect. This is made possible by explicitly satisfying the Baym criterion for the macroscopic conservation of particle‐number, momentum and energy—a criterion not satisfied by any of the earlier Green’s function treatments of the Kondo model or the Anderson model. The free energy of the system is calculated and the universality of all the thermodynamic properties including resistivity is analytically demonstrated. The temperature‐dependent susceptibility χ(T) and specific heat C(T) thus calculated are found to be almost indistinguishable from the results of the renormalization group theory.

Correlation Energy and the One‐Center Coulomb Repulsion Integral

A distinction is made between the various contributions to the difference between theoretical and empirical values of correlation energy associated with the two-pi-electron system. (P.C.H.)

Cluster Expansion of an Inverse Overlap Matrix for Solids

In this paper, a method is developed to compute an inverse overlap matrix based on a linked cluster expansion of a determinant. The inverse is expanded in terms of cluster integrals represented by diagrams and a recurrence relation for generation of all diagrams required is found. Thus the computation of an exact inverse overlap matrix is reduced to solving the recurrence equations self‐consistently. An approach for solving the equations is suggested and bounds for errors accompanying this procedure are calculated. The method is applied to the hydrogen lattice.

New many body perturbation method and the Hubbard model

Abstract By adapting the functional derivative method developed by Kadanoff and Baym to the Hubbard model, a new perturbation method is formulated. The unperturbed state is defined by the two equations which yield Hubbards results, while the remainder is given by functional derivatives of the Greens functions which are shown to generate a complete perturbation series. Advantages of this method are discussed.

Insulating states and metal‐nonmetal transition in the Hubbard model

If a band is narrow and is not nearly empty or nearly full, the Hubbard lattice is an insulator. A nearly half‐filled lattice is a Hubbard‐type insulator with a gap but if the number of electrons decreases or increases beyond a certain limit, the lattice becomes a ’’gapless’ insulator. As the bandwidth increases, these insulating states will turn metallic. The mechanism involved in the transition is presented.

The Kondo effect in the Anderson model

We show that the Green’s function solution of the Anderson model calculate by the functional derivative method developed earlier yields a density of states having the three‐peak structure proposed by Gruner and Zawadowski and that the central peak indeed introduces the lnT dependence.

Excitation spectrum of a magnetic spiral structure in a hexagonal lattice

A magnetic spiral structure with propagation vector Q parallel to a hexagonal crystal axis (as exhibited by holmium metal) is perturbed by the hexagonal crystal field anisotropy, introducing modulations Q+or-6Q. By calculating spin deviations from the modulated spiral, the spin Hamiltonian is generated. The Hamiltonian exhibits interactions between the modes omega (q) and omega (q+or-6Q), but is shown to be diagonalized in terms of a new set of independent modes by a novel, non-unitary transformation. Numerical results, which are obtained by using exchange coupling parameters determined at higher temperature (where the hexagonal field is negligible) predict the change in the shape of the spin wave spectrum of holmium at lower temperatures where the field effect is appreciable. From the spin wave spectrum the magnetic zero-point motion is evaluated, and this is found to be larger along the hard directions of the hexagonal plane than along the easy directions. The corresponding modulation of the effective magnetic moments has been calculated numerically for holmium, and found to be consistent with recent experimental observations.

Temperature Dependence of Spin Structures Under the s‐f Interaction

A system of spins interacting through the s‐f exchange coupling may exhibit an antiferromagnetic screw structure with temperature‐dependent pitch parameter Q, but transform to a ferromagnetic state at a lower temperature. This behavior is shown to be explained by temperature‐dependent distortion in the shape of the Fermi surface. The expression for the number operator which determines the chemical potential μ and the Fermi surface is calculated by the Greens function technique. A simple second‐order perturbation treatment gives the expression involving a Kondo‐like integral and yields the desired temperature dependence in kf in appropriate directions.