Strongly correlated electron systems are studied with the help of periodic Anderson model (PAM). The PAM in which highly correlated nondegenerate localized states form a subsystem is considered and the focus of study is on magnetic ordering of electrons in these localized states. In order to study the PAM, which is not amenable to exact solution, two approximate schemes are proposed. The first one is called the spectral density approximation (SDA). Guided by the atomic limit, a two-pole ansatz is made for the localized electron spectral density. The spectral weights and the quasiparticle energies are determined by a moment method. From the spectral density, the spin and energy dependent self-energy is evaluated. A principal limitation of this method is that per ansatz, the quasiparticles are of infinite lifetime. To introduce a finite lifetime, a second approximation scheme is proposed where coherent potential approximation (CPA) is applied to PAM. In order to do CPA, an alloy analogy (AA) is required. In the conventional AA, the concentrations α and the atomic levels E of the fictitious alloy are taken from the atomic limit. Since the interest is in the magnetic properties, this AA is not appropriate. Therefore, a modified AA (MAA) is proposed. In MAA, α and E are obtained using the high energy expansion of the Green's function and the self-energy. In both the approximations, the density of states and the magnetization are selfconsistently evaluated and a phase diagram is obtained. Comparison of the results of the two schemes brings out the effect of quasiparticle damping on the magnetic properties.
Ferromagnetism in the periodic Anderson model. A comparison of spectral density approximation (SDA), modified alloy analogy (MAA) and modified perturbation theory (MPT)