Green's Function Theory for the Anderson Model

概要

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The Anderson model is considered using a new Green's function formalism which is proposed by Sawada. An exact solution of the approximate t-matrix integral equation is obtained when E+U/2=0, where E is the extra localized orbital energy and U is the Coulomb energy in the Anderson model. The t-matrix is given by t(z)=(z-3F(z))/(z^2-4F(z)z+3F(z)^2-U^2/4), where F(z)=Σ__k(V^2_<dk>)/(z-ε_k) The ensemble average of d-electron number of spin up is shown self-consistently to equal to that of spin down and both average exactly one half. The exact solution for the t-matrix differs in its temperature independence from the usual s-d exchange model. The conductivity σ, thermoelectric voltage θ, specific heat Δc and susceptibility x are calculated using the exact solution. At low temperatures, σ∝a+bT^2+ct^4,θ∝eT/(1+fT^2)+…,Δc∝g/T(1-thq/t),x∝A+BT^2 where a,b,c, etc., are constants. At higher temperatures, the susceptibility follows the Curie-Weiss law.
理論物理学刊行会の論文
1970-02-25