# Ground State of a Semiconductor-like System with Transverse s-d Interaction and Perturbation Method†)

Progress of Theoretical Physics, May 1970

Application of perturbation method to the ground state of a semiconductor-like system with transverse s-d interaction is accompanied by a serious difficulty of logarithmic divergence similar to that of the ordinary s-d problem, as the width of the forbidden band, Δ, goes to zero. As a preliminary study to improving Abrikosov approximation by considering less divergent terms, it is here attempted to remove just the logarithmic divergence of the second order term of the ground state expectation value of the longitudinal component of a localized spin, ≪ Sz >. For this object, an approximate perturbational ground state wave function is constructed from the Rayleigh-Schrödinger perturbational wave function, by expecting that the weight of many-electron excited configurations should increase with decreasing Δ. The obtained ≪ Sz > is markedly different from the result of the second order perturbation theory and gradually tends to zero as Δ→0, statisfying the physical condition 0 ≤≪ Sz > ≤S all over the region of Δ. On the other hand, the obtained expectation values of the energy ≪H> and the number of the excited electrons ≪n>> coincide essentially with those of the second order perturbation theory. The present approximation may be regarded as the furthest extreme very opposite to Abrikosov approximation in which only the diagrams consisting of just one closed loop of particle line are summed up. (See Fig. 3.) The truth is expected to lie between the two approximations.

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Itsuo Ohnari, Koji Ishikawa, Yukio Mizuno. Ground State of a Semiconductor-like System with Transverse s-d Interaction and Perturbation Method†), Progress of Theoretical Physics, 1970, 1186-1198, DOI: 10.1143/PTP.43.1186